Test of Statistics 6 RoeLee 3.1 Author: John S Fry Date: … · 2018. 4. 5. · 6.1 descriptive statistics 6.2 2-group t-test 6.3 welch test 6.4 fisher-pitman test 6.5 dunnett test

Test of Statistics 6 RoeLee 3.1

Author: John S Fry

Date: 11/6/2007

Version: 1.0 Authorised by: Date authorised:

t:\rldocs\tstats\tstats6.doc

ROELEE

___________________________________________________________________________ TEST OF STATISTICS 6

RL 3.1

A general computer system for recording and analysing data, with special provision for necropsy and histopathology

TEST OF STATISTICS 6

RoeLee 3.1

June 2007

TEST OF STATISTICS 6

RoeLee 3.1 ___________________________________________________________________________

ROELEE Documentation

© Copyright 2007, P.N.Lee Statistics and Computing Ltd. 17 Cedar Road, Sutton, Surrey SM2 5DA. Tel: 020-8642-8265

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TEST OF STATISTICS 6 - CONTENTS

1. INTRODUCTION

2. AHNER-PASSING PROCEDURE

3. BONFERRONI ADJUSTMENTS

4. LÜDIN PROCEDURE

6. PARAMETRIC STATISTICS

6.1 DESCRIPTIVE STATISTICS

6.2 2-GROUP T-TEST

6.3 WELCH TEST

6.4 FISHER-PITMAN TEST

6.5 DUNNETT TEST

6.6 LEVENE TEST

6.7 BONFERRONI ADJUSTMENTS

6.8 LÜDIN PROCEDURE

7. NON-PARAMETRIC STATISTICS


7.2 WILCOXON TEST

7.3 KRUSKAL-WALLIS TEST

7.4 STEEL TEST

7.5 JONCKHEERE TEST



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8. TEST OF 2xk TABLES


8.2 FISHER EXACT TEST

8.3 CHI-SQUARED TEST

8.4 AHNER-PASSING TEST

8.5 TREND TESTS



9. ANALYSIS OF COVARIANCE AND REGRESSION

10. CONDITIONAL TESTS IN COMMAND FILES

11. REFERENCES

______________________________________________________________________

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APPENDICES

1A. AHNER-PASSING TABLES

1B. AHNER-PASSING MODULE

2A. BONFERRONI RESULTS

2B. BONFERRONI MODULE

3A. COMMAND FILE TSTATS1.CMD

3B. RESULTS FROM TSTATS1.CMD

4A. COMMAND FILE TONEWAY.CMD

4B. RESULTS FROM TONEWAY.CMD

4C. EXTRND ROUTINE

4D. PERMUTATIONS USED IN FISHER-PITMAN TEST EXAMPLE

4E. EXTRA DUNNETT TABLES

4F. COMMAND FILE TLEVENE.CMD

4G. RESULTS FROM TLEVENE.CMD

5A. COMMAND FILE TKWALL.CMD

5B. RESULTS FROM TKWALL.CMD

5C. EXTRA STEEL TABLES

5D. TESTS OF JONCKHEERE FOR SMALL NUMBERS

5E. JONCKHEERE MODULE

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6A. COMMAND FILE TEXACT.CMD

6B. RESULTS FROM TEXACT.CMD

6C. COMMAND FILE TCHI2.CMD

6D. RESULTS FROM TCHI2.CMD

7A. COMMAND FILE TACOVA.CMD

7B. RESULTS FROM TACOVA.CMD

7C. GLIM BATCH FILE

7D. RESULTS FROM GLIM BATCH FILE

8A. COMMAND FILE TOWKW.CMD

8B. RESULTS FROM TOWKW.CMD

______________________________________________________________________

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1. INTRODUCTION

For version 3.1 of RoeLee, extra statistical procedures have been introduced which allow for analysis of even more types of data, particularly that from in-life datasets. This document explains the procedures and algorithms used in this work, giving detailed workings where possible. Some procedures, such as the Ahner-Passing or the Lüdin procedure are used in several tests and these are reported in their own sections. ______________________________________________________________________

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2. AHNER-PASSING PROCEDURE

In their paper, "Berechnung der multivariaten t-Verteilung und simultane Verleiche gegen Kontrolle bei ungleichen Gruppen- besetzungen"1, Ahner and Passing describe a method for generating probabilities when there are multiple comparisons versus a control group. In particular, the method should calculate the probabilities for the Dunnett test, the Steel test and the Ahner-Passing test, all of which were required for the Datatox F1 Advanced Statistics. In addition to describing the method the paper gave a Fortran program for calculating the probabilities together with tables for the Dunnett test and for the Studentized maximum. This program was entered into a computer, with some minor changes to make it nearer to the method as described, but when the program was run it failed to generate the tables given in the paper. On closer inspection of the paper it was realised that the paper used a 16-point Cauchy integration formula, whereas the tables were generated using a 48-point Cauchy integration formula. Fortunately we had access to the same book they used, Handbook of Mathematical Functions, edited by Abramowitz and Stegun2, and the 48-point formulae were inserted instead. This produced essentially the same results as in their paper - see below for details. Another problem encountered was that the formulae for the Steel test and for the Ahner-Passing test both used infinite degrees of freedom and it was uncertain how best to use the program to generate these. Two ideas were tried, one to put in a very large degrees of freedom and see how close the answers came to those required, and the other to try to solve the equations as degrees of freedom tended to infinity and use those solutions instead. Now, from equation (15) of the paper: bf - af ξ(z) = ------- (z+1) + af 2 = √(f/2)[ [ √[1+5√(2/f)] - √[1-5√(2/f)](z+1)/2 + [√[1-5√(2/f)] ~ √(f/2) [ 5√(2/f)(z+1)/2 + 1 - 5√(2/f) /2 + 25(2/f) /8 - ... ~ √(f/2) [5 √(2/f) z/2 +1] ~ 5z/2 + √(f/2) Hence, ξ(z)/√f ~ √(1/2) as f -> infinity Now, bf - af ~ √(f/2)[5√(2/f)] = 5 c(z) ~ ξ(z) / √(f/2) ~ 1 + (5z/2)√(2/f)

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Then equation (19) becomes: h(z) ~ (5/2π)√(1- 2/f) . exp[ -(f/2)[1 + 2(5z/2)√(2/f) +(25z2/4)(2/f) -1 +ln(1- (2/f)) ] -1 + (f-1)[(5z/2)√(2/f) + (25z2/4)(2/f) + ...]

~ (5/2π) exp [ -(f/2)[ 5z√(2/f) + (25z2/4)(2/f) - (2/f) ]

-1 + f [(5z/2)√(2/f) + (25z2/4)(2/f)]

- [(5z/2)√(2/f) + (25z2/4)(2/f)]

~ (5/2π) exp [ -5z√(f/2) -25z2/4 +5z√(f/2) +25z2/2 -(5z/2)√(2/f) ] ~ (5/2π) exp [ -25z

2/2 ]

while equation (11) becomes δi(ξ,v) ~ (λ/√2 + civ ) / √(1 - ci

2) hence √2. δi ( ξ(z), 5w/√2) ~ ( λ + 5wci )/ √(1 - ci

2 ) These new equations for the solution for infinite degrees of freedom were used in the program when the degrees of freedom were set to -1, with 32000 used as the large degrees of freedom in the original equations for comparison. The program was then set to reproduce all the tables in the Ahner-Passing paper, and also to produce the tables from the 2 Dunnett papers, "A Multiple Comparison Procedure for Comparing several Treatments with a Control"3, and "New Tables for Multiple Comparisons with a Control", 4. In addition, the tables to compare with those from the Steel paper, "A Multiple Comparison Rank Sum Test: Treatment versus Control"5, were also produced. The results are given in Appendix 1A, with differences between the results and the various papers marked. It is clear that there is general agreement between the results, but there are some differences. The results were checked against the Ahner-Passing and Dunnett papers mentioned above and against the table of Percentage Points of the t-Distribution given in Abramowitz and Stegun, "Handbook of Mathematical Functions", 2. This last table was used to check the values for a single comparison group i.e. column 1 of the tables given in Appendix 1A. This table gave values to 3 decimal places. Where differences were found they were in the third decimal place, the value differing by .001 each time. The statistical papers gave results to 2 decimal places and so the results given in Appendix 1A were rounded before comparison. Whenever a result disagreed with the Abramowitz and Stegun tables, it agreed with the values given in the statistical papers.

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Similarly for the other columns, whenever a result disagreed with one of the papers and the result could be checked against a second paper, the second paper agreed with the result and disagreed with the first paper. The exception to this was in the result for Dunnett's test, one sided with alpha = 0.01, for 5 comparison groups and 14 degrees of freedom. Both papers gave the value 3.32 but the result in Appendix 1A is 3.326, that is, only an error in the third decimal place. Some parts of the results tables could be checked against only one statistical paper. Here the number of differences was small and consistent in number with those parts which were checked against two papers (where only one of the papers disagreed with the results). Each difference was in the last decimal place of the value given in the paper and differed by .01 (given that the results were rounded to 2 decimal places). One of these differences was with table 2.2 in the Ahner-Passing paper. This gives 3.10 as the value for 11 comparison groups with 13 degrees of freedom. This value cannot be correct because it conflicts with fact that the values for a column must decrease monotonically as the degrees of freedom increase. The values above this in the column are 3.05 for 12 degrees of freedom and 3.09 for 11 degrees of freedom. The value would have agreed with the results in Appendix 1A and would have been monotonically decreasing if the last two digits had been reversed i.e. 3.01. This appears to be a typographical error. Thus it is possible that other differences are due to errors in the Ahner-Passing paper. The results from the Steel test are very different for larger numbers of control groups, but this is because Steel was using the figures Dunnett gave in his first paper, which he admitted were only very approximate. A copy of the Fortran program for the Ahner-Passing routine is included in Appendix 1B. Note that in subroutine quag2e logs were taken and added together, rather than multiplying up the raw figures in order to keep a control on possible underflow errors. ______________________________________________________________________

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3. BONFERRONI ADJUSTMENTS Bonferroni adjustments are adjustments made to probabilities in order to take account of multiple testing. In this form of adjustment all the information that is needed is the number of comparisons being made and the probabilities themselves. There have been many adjustments of this form put forward, but we have decided to allow for 4 different adjustments: 1) The standard Bonferroni adjustment, where the probability is shared equally across all

comparisons, that is

let Pi be the p-values corresponding to hypotheses Hi then if there are m hypotheses, and the overall size of the test = α,

reject Hi when Pi <= α/m 2) Bonferroni-Holm α adjustment - see Hochberg, "A Sharper Bonferroni procedure for

multiple tests of significance"6: let p(1),..., p(m) be the ordered p-values, with H(1),... H(m) the corresponding hypotheses then reject H(i) when for all j=1,...,i p(j) <= α/(m-j+1) 3) Hochberg-Hommel α adjustment - see Hommel, "A comparison of two modified

Bonferroni procedures"7: let p(1),..., p(m) be the ordered p-values, with H(1),... H(m) the corresponding hypotheses let J = {i' such that p(m-i'+k) > k.α/i',k=1,..,i' } then reject Hi when pi <= α/j', with j'=max J if J empty, reject all Hi, i=1,..,m 4) Hochberg procedure - see Hochberg and Benjamini, "More powerful procedures for

multiple significance testing"8.

Generally one proceeds from the highest to the lowest p-values retaining H(i) if its p-value satisfies p(i) > α/(m-i+1). One stops the procedure at the first ordered hypothesis with lower or equal p-values.

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One problem in putting these procedures into RoeLee is that RoeLee usually presents probabilities as <0.1, <0.05, <0.01 and <0.001. Thus one will be interested in which of these levels the probability has been adjusted to by the procedure. Thus the adjusted probabilities are set at just less than the smallest level at which they would be significant. That is, if the adjusted probability would have been significant at the 0.05 level, but not at the 0.01 level, the adjusted probability was set at 0.0499999. Where the adjusted probability would not even be significant at the 0.1 level, the probability was set to 1.0. The exception to this was for simple Bonferroni adjustments, where an actual adjusted probability of m times the actual probability can be calculated. If this adjusted probability was significant at the smallest possible level, 0.001, the adjusted probability was left with this level. For example, if the original probability was 0.0001 and there were 3 hypotheses to be tested, the adjusted probability would be given as 0.0003, not 0.00099999. Note that the same principal can be applied to the Bonferroni-Holm adjustement. This is essentially a stepdown procedure, where the effect is to multiply the smallest probability by the number of hypotheses being tested (just as in a usual Bonferroni adjustement). However, the next smallest probability is multiplied by the the number of hypotheses left to be tested, that is the number is reduced by one. This continues until the final comparison is not adjusted at all. Note that we insist that the adjusted probability at each stage cannot be less than that at the previous stage. Thus we can present effective adjusted probabilities for the Bonferroni and the Bonferroni-Holm procedures, and the system allows for this by setting the system message S0006 column 27 to “2”. This is particularly useful when checking results against those given in SAS or SPSS. The probabilities from the Hochberg and Benjamini paper were used as input to the subroutine BonfAdj and the resulting adjusted figures are given in Appendix 2A. They appear in agreement with the discussion in the paper, but do not seem to give different enough results to show differences between the different tests. The module itself is given as Appendix 2B. ______________________________________________________________________

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4. LÜDIN PROCEDURE Lüdin, in his paper "A test procedure based on ranks for the statistical evaluation of toxicological studies"9, put forward a procedure in which a trend test is used repeatedly, in each case significance being interpreted as showing the top dose as being significant. The top dose is then ignored and the trend test re-run on less and less groups until there are no comparison groups left or no significance is found. Then any remaining groups are tested for heterogeneity, and if significance found 2-group comparisons are performed. In Lüdin's paper, the Jonckheere test was recommended for the trend test, Kruskal-Wallis for the heterogeneity and Mann-Whitney U-test for the 2-group comparison. Banken, in a paper given to the Working group for statistics in F1, has pointed out that the approach should generalise to any trend, heterogeneity and 2-group comparison test. In RoeLee, a single analysis of a variable would normally entail doing all 3 types of test and so it seemed that the best approach would be to develop a general procedure in RoeLee for this type of analysis. The only theoretical problem is that RoeLee presents all probabilities from an analysis. That is, if users ask for a Kruskal-Wallis analysis and 2-group analyses, the probabilities shown will be those from doing all the chosen analyses and not the alternative of assigning the probabilities of the 2-group analyses to non-significance when the heterogeneity test gives a non-significant answer. The procedure has been introduced for analysis of variance, in both parametric and non-parametric forms, Fisher's exact analyses and for Chi-squared analyses, including full Peto Log-rank. In each case, where more than one form of a particular analysis is available, users can choose between them. For example, users can choose to use the Jonckheere trend test or the Fry-Lee trend test when doing non-parametric analyses of Variance. T-tests can be any of the 4 forms available - using all group variance, using 2-group variance, using the Welch test or using the Fisher-Pitman test. Users can specify the level for the trend test as 0.1, 0.05, 0.01 or 0.001. Testing of these procedures was done by having the program calculate all the trend, heterogeneity and 2-group comparisons missing out successive top dose levels and then checking that the results from the Lüdin procedure agreed with these calculations. See the sections below for each of these tests (6.8, 7.6 and 8.7). ______________________________________________________________________

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6. PARAMETRIC STATISTICS Parametric statistics are organised around the keyword ONEWAY and the routines pdescb in module NONP.FOR and oneway3 in module ONEWAY.FOR. The command file, TONEWAY.CMD, given in Appendix 3B, has been written to produce test results from the RoeLee Worked Example based on the following data: Animal Sex Group Sodium Potassium 1 1 1 150.0 3.82 2 1 1 148.1 3.93 3 1 1 150.3 3.79 4 1 1 149.9 3.80 5 1 1 150.6 3.25 6 1 1 153.2 3.31 7 1 1 148.3 4.17 8 1 1 152.5 3.34 9 1 1 148.9 3.53 10 1 1 148.4 3.72 11 2 1 145.3 3.68 12 2 1 147.4 3.52 13 2 1 145.1 3.36 14 2 1 -4 -4 15 2 1 145.7 3.25 16 2 1 144.5 3.55 17 2 1 146.3 3.50 18 2 1 147.2 3.52 19 2 1 145.3 3.50 20 2 1 144.0 4.04 21 1 2 145.9 3.56 22 1 2 147.6 3.53 23 1 2 150.9 3.76 24 1 2 145.5 3.80 25 1 2 146.9 3.36 26 1 2 146.6 3.57 27 1 2 143.8 3.34 28 1 2 144.1 3.77 29 1 2 140.6 3.68 30 1 2 137.5 3.60 31 2 2 147.9 3.51 32 2 2 145.4 3.78 33 2 2 141.5 3.29 34 2 2 141.8 3.19 35 2 2 138.0 2.60 36 2 2 142.9 3.37 37 2 2 127.4 2.86 38 2 2 140.9 3.09 39 2 2 142.6 3.13 40 2 2 146.4 4.04

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Animal Sex Group Sodium Potassium 41 1 3 138.0 3.41 42 1 3 139.8 3.60 43 1 3 147.9 3.53 44 1 3 146.7 3.47 45 1 3 145.8 3.73 46 1 3 145.3 4.59 47 1 3 144.5 3.61 48 1 3 149.9 4.08 49 1 3 148.5 4.02 50 1 3 148.5 3.76 51 2 3 134.4 3.46 52 2 3 132.1 2.77 53 2 3 142.2 3.79 54 2 3 148.9 4.37 55 2 3 147.1 3.43 56 2 3 149.5 3.35 57 2 3 150.2 3.85 58 2 3 146.3 3.42 59 2 3 148.1 3.57 60 2 3 148.1 3.07 61 1 4 141.8 3.58 62 1 4 143.8 3.87 63 1 4 145.4 3.57 64 1 4 135.7 3.07 65 1 4 145.1 3.40 66 1 4 143.6 4.20 67 1 4 144.4 3.64 68 1 4 142.4 3.20 69 1 4 143.6 3.46 70 1 4 142.9 3.73 71 2 4 149.3 3.40 72 2 4 148.5 4.24 73 2 4 147.4 3.55 74 2 4 149.4 3.61 75 2 4 144.4 4.41 76 2 4 149.7 3.68 77 2 4 148.3 3.77 78 2 4 145.8 4.05 79 2 4 145.6 3.60 80 2 4 146.0 3.38 Note that the value -4 refers to missing values. The results from running the command file are given in Appendix 4B. ______________________________________________________________________

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6.1 DESCRIPTIVE STATISTICS The following descriptive statistics are calculated in this form of analysis: Note we include the RoeLee descriptors for each statistic used. Statistic Description 1 N number of observations

The number of non-missing observations in each group and optionally the total over groups is given.

2 Mean Arithmetic mean x blank if n = 0,

∑= ixn

x 1 otherwise

3 St.Dev Standard deviation s blank if n <2, otherwise:

( )∑ −−

= 22

11 xx

ns i

4 St.Err Standard error of mean xs blank if n <2, otherewise:

nssx = 14 GMean Geometric mean – undefined if any values <= 0, else: G ∏= i

n xG 15 HMean Harmonic mean – undefined if any values = 0, else:

H ∑

=

ixnH 1

11

21 CoefV Coefficient of Variation

xsCV 100=

23 %dev Relative Group Mean Difference For group j versus control group (c):

( )

c

cj

xxx

dev−

= 100%

31 Skew Skewness

This value attempts to quantify aspects of asymmetry of a distribution about its mean. Positive values indicate

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distributions skewed to values greater than the mean, negative values to distributions skewed to values less than the mean.

( )( )∑ ⎟⎠⎞

⎜⎝⎛ −

−−=

3

21 sxx

nnnSkew i

32 Kurt Kurtosis

This characterises the relative peakedness or flatness of a distribution compared to a Normal distribution – positive values indicate a relatively peaked distribution, negative values indicate a relatively flat distribution.

( )( )( )( )

( )( )( )32

13321

1 24

−−−

−⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛ −

−−−+ ∑ nn

ns

xxnnn

nn i

Note the skewness and kurtosis parameters have only been included to allow checking against other systems (particularly SAS and SPSS). To have them appear on output users must set the system message S006 such that: Column 24: <=1 for no skewness, 2 to include Column 25: <=1 for no kurtotis, 2 to include and also ensure that standard deviations have been requested in the output.

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The results for Sodium at 6 months, males, are given in Appendix 4B, Table 1. Now for Sodium at 6 months, Males: Group 1 Values LOG INVERSE Sum Sqs 1 148.10 4.9978877 .00675219440 2 148.30 4.9992372 .00674308830 3 148.40 4.9999113 .00673854440 4 148.90 5.0032749 .00671591670 5 149.90 5.0099684 .00667111400 6 150.00 5.0106353 .00666666666 7 150.30 5.0126333 .00665335990 8 150.60 5.0146273 .00664010620 9 152.50 5.0271646 .00655737700 10 153.20 5.0317443 .00652741510 SUM 1500.2 50.1064102 0.06666578266 225087.22 Mean 150.02 5.01064102 0.006666578266 Var 3.024 Parametric descriptors B.1 n 10 B.2 Mean 150.02 B.3 SDev 1.73896521 B.4 SErr 0.549909083 B.14 G 150.0008589 B.15 H 150.001989 B.21 CV 100*SDev/mean = 1.159155586 B.23 %dev blank

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Group 2 Values LOG INVERSE Sum Sqs 1 137.50 4.923623917 .00727272727 2 140.60 4.956918979 .0071123755 3 143.80 4.968423445 .0069541029 4 144.10 4.970507503 .0069396252 5 145.50 4.980176087 .0068728522 6 145.90 4.982921455 .0068540095 7 146.60 4.987707789 .0068212824 8 146.90 4.989752083 .0068073519 9 147.60 4.994505912 .0067750677 10 150.90 5.016617366 .0066269052 Sum 1449.4 49.76015453 .0690363 210202.66 Mean 144.94 5.01064102 .006666578266 Var 14.06933333 Parametric descriptors B.1 n 10 B.2 Mean 144.94 B.3 SDev 3.750911 B.4 SErr 1.186142206 B.14 G 144.8958855 B.15 H 144.8513315 B.21 CV 100*SDev/mean = 2.58790603 B.23 %dev (mean / control mean -1)*100 = -3.386215172

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Group 3 Values LOG INVERSE Sum Sqs 1 138.00 4.927253683 .0072463768 2 139.80 4.94021283 .0071530758 3 144.50 4.973279507 .0069204152 4 145.30 4.97880057 .0068823124 5 145.80 4.982235819 .0068587105 6 146.70 4.988389685 .0068166325 7 147.90 4.99653637 .0067613252 8 148.50 5.000584958 .0067340067 9 148.50 5.000584958 .0067340067 10 149.90 5.009968405 .006671114 Sum 1454.9 49.79784679 .068777976 211807.83 Mean 145.49 4.979784679 .0068777976 Var 14.93655555 Parametric descriptors B.1 n 10 B.2 Mean 145.49 B.3 SDev 3.864784024 B.4 SErr 1.222152018 B.14 G 145.4430613 B.15 H 145.3953802 B.21 CV 100*SDev/mean = 2.6563915 B.23 %dev (mean / control mean -1)*100 = -3.0195973

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Group 4 Values LOG INVERSE Sum Sqs 1 135.70 4.910446567 .0073691967 2 141.80 4.954417614 .0070521861 3 142.40 4.958639999 .0070224719 4 142.90 4.962145085 .0069979006 5 143.60 4.967031657 .0069637883 6 143.60 4.967031657 .0069637883 7 143.80 4.968423445 .0069541029 8 144.40 4.972587226 .0069252077 9 145.10 4.97742316 .0068917987 10 145.40 4.979488565 .006877579 Sum 1428.7 49.61763497 .07001802 204186.79 Mean 142.87 4.961763497 .007001802 Var 7.602333333 Parametric descriptors B.1 n 10 B.2 Mean 142.87 B.3 SDev 2.757232912 B.4 SErr 0.871913604 B.14 G 142.8454815 B.15 H 142.8203756 B.21 CV 100*SDev/mean = 1.9298893 B.23 %dev (mean / control mean -1)*100 = -4.7660311 ______________________________________________________________________

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6.2 2-GROUP T-TEST The usual RoeLee version of the Student t-test is based on using the variance for all groups being analysed. This is explained in detail in Test of Statistics, section 3. For some clients, it was required that the t-test was to be based only on the pooled variance of the 2 groups being compared. Thus here the test statistic T for comparing group i with the control group, here say group 1, is derived from:

( )[ ]1

1

11 nnsxx

Ti

i

+

−=

where ni = number of observations for group i ix = mean for group i is = standard deviation for group i ( ) ( )[ ] ( ) ( )[ ]1111 1

211

22 −+−−+−= nnsnsns iii (See Winer, BJ "Statistical Principles in Experimental Design"10) Now, referring back to the previous section, for sodium at 6 months, males: ni 10 10 10 10 xi 150.02 144.94 145.49 142.87 si 1.73896521 3.750911 3.864784024 2.757232912 si

2 3.024 14.06933333 14.93655555 7.602333333 s2 8.546666665 8.980277775 5.313166667 T 3.885530581 3.380168257 6.936083685 F=T2 15.0973479 11.42553745 48.10925688 P P<.004 P<.01 P<.00002 These results agree with Appendix 4B, Table 1, to full 6 decimal place accuracy. Note that when comparing with the results in Appendix 4B, F, which in this case is equivalent to T2, rather than T is given. Also the actual probabilities are computed rather than just table lookups on critical values. (Note the critical values were taken from the "Handbook of Mathematical Functions" edited by Abramowitz and Stegun2.)

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For females, we shall use the means and standard deviations computed by the program and given in Appendix 4B, Table 2. This gives: Group 1 2 3 4 ni 9 10 10 10 xi 145.644444 141.48 144.69 147.44 si 1.144674 5.723791 6.441782 1.875692 si

2 1.3102786 32.761783 41.4965553 3.5182205 s2 17.96107505 22.5853883 2.4791890 T 2.138628 0.437101 2.481925 F=T2 4.573731 0.191057 6.159950 P P<0.1 P>0.4 P<0.1 Note that as the standard deviations were only given to 6 decimal places, the final accuracy is only to 5 decimal places. ______________________________________________________________________

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6.3 WELCH TEST Welch, BL, in his paper, "The generalization of "Student's" Problem when several different population variances are involved"11, put forward a solution to the problem when the assumption of equal variances for groups when performing a t-test does not hold. In particular, he noted that there was a good approximate answer by using the same procedure as in the usual Student t-test, but looking up the tables with an adjusted degrees of freedom, where f = adjusted degrees of freedom for comparing group i with control group (1)

( )

( ) ( )11 1

21

21

22

21

21

2

−+

−

+=

nns

nns

nsns

i

ii

ii

The T statistic is in a slightly different form for this test:

( )

[ ]121

2

1

nsns

xxT

ii

i

+

−=

where ix and is are as defined in 6.2. Note, when inn =1 , the T statistics in 6.2 and 6.3 are the same. Thus for Sodium at 6 months, males, we need only to recompute the degrees of freedom: ni 10 10 10 10 xi 150.02 144.94 145.49 142.87 si 1.73896521 3.750911 3.864784024 2.757232912 si2 3.024 14.06933333 14.93655555 7.602333333 s2 8.546666665 8.980277775 5.313166667 T 3.885530581 3.380168257 6.936083685 F=T2 15.0973479 11.42553745 48.10925688 f 12.698 12.501 15.182 P P<.004 P<.01 P<.0002

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While for females: Group 1 2 3 4 ni 9 10 10 10 xi 145.644444 141.48 144.69 147.44 si 1.144674 5.723791 6.441782 1.875692 s12 1.3102786 32.761783 41.4965553 3.5182205 s2 17.96107505 22.5853883 2.4791890 T 2.251293 0.460529 2.545906 F=T2 5.068318 0.212087 6.481636 si2 /ni .145586511 3.2761783 4.14965553 0.35182205 (si2 /ni)2 .021195432 10.733344 17.219641 0.12377875 /(ni-1) .002649429 1.192594 1.9132931 0.01375319 f 9.797 9.629 15.084 P P<0.1 P>0.4 P<0.1 ______________________________________________________________________

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6.4 FISHER-PITMAN TEST As of now, no information has arrived at PNLSC concerning this test, but as it was described as a permutation form of t-test there seemed to be only one sensible way to perform it: Take the statistic, ixxT −= 1 and calculate the probability that under permutations of the data between the 2 groups, values of less than or equal to the observed value would have been achieved. Now the data values would be unchanged in all permutations, only the group that they belonged to would change. Thus Σ xj over the 2 groups will be a constant, S, say. Then, T = (1 / n1 ) Σ x1j - (1 /ni ) Σxij S = Σ x1j + Σ xij T = (1/n1 ) Σ x1j - (1/ni) (S - Σ xij ) = - (1/ni)S + [(1/n1) + (1/ni) ] Σ x1j As for each permutation, S, n1 and ni are constant, T depends only on Σ x1j and thus we can consider just the values of Σx1j over each permutation of the data between groups. RoeLee already has an algorithm to deal with calculating the probabilities involved in this process, which has been used extensively in calculations of Fisher Exact trend tests and is also used in calculating exact probabilities for 2-group Wilcoxon tests. The routine, ExTrnd, is given as Appendix 4C. Below, we give details of calculating the permutation test for Sodium at 6 months, group 1 versus group 2. In Appendix 4D we give a printout of the actual permutations used when testing the program. To calculate 2-sided probabilities, we have used the standard RoeLee method of taking twice the minimum probability. It may be possible to adapt this procedure to calculate the probability as the sum of all probabilities less than the observed probability, though I doubt this has the appropriate meaning in this case.

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Now, for sodium at 6 months, males: Total observed for controls = 1500.2 There are 20C10 permutations possible = 184756 Only the 10th value in group 2 is larger than any values of group 1, replacing group2 (10) with 1-8 should increase total by 2.8 to 0.3 units as group 2(9) - group1(1) is 0.5 units We now list the following possible permutations - note that it is possible to end up with the same permutations in 2 places, for instance: 2(10) -> 1(8), 2(9) -> 1(1) is the same permutation as 2(10) -> 1(1), 2(9) -> 1(8). Such similar permutations have been marked by a "X". A final "1" marks permutations that should count in the the overall probability: Observed Tables, T= 1500.2 1 2(10) -> 1(8), T -> T + 0.3, 2(9) -> 1(1), T-> T -0.2 X 1 1(7), T -> T + 0.6, 2(9) -> 1(1), T-> T +0.1 X 1 1(6), 0.9, 2(9) -> 1(1), 0.4 X 1 2(8) -> 1(2) -1.1 2(9) -> 1(2), 0.2 X 2(9) -> 1(3) 0.1 X 2(9) -> 1(4) -0.4 1(5), 1.0, 2(9) -> 1(1) 0.5 X 1 1(2) 0.3 X 1(3) 0.2 X 1(4), 2.0, 2(9) -> 1(1), 1.5 X 1 2(8) -> 1(2) 0.1 X 2(9) -> 1(2) 1.3 X 2(8) -> 1(1) 0.1 X 2(9) -> 1(3) 1.2 X 2(8) -> 1(1) 0.0 X 2(9) -> 1(5) -0.3 2(8) -> 1(1) 0.8 X 2(7) -> 1(2) -0.9 2(8) -> 1(2) 0.6 X 2(8) -> 1(3) 0.5 X 2(8) -> 1(5) -1.0 2(7) -> 1(1) 0.5 X 2(7) -> 1(2) 0.3 X 2(7) -> 1(3) 0.2 X 2(7) -> 1(5) -1.3 2(6) -> 1(1) -0.2 1(3), 2.5, 2(9) -> 1(1) 2.0 X 1 2(8) -> 1(2) 0.6 X 2(7) -> 1(4) -1.7 2(8) -> 1(4) 0.0 X 2(7) -> 1(2) 0.3 X 2(7) -> 1(4) -0.3 2(6) -> 1(2) -0.4 2(9) -> 1(2) 1.8 X 2(8) -> 1(1) 0.6 X

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2(7) -> 1(4) -1.7 2(8) -> 1(4) -0.2 2(7) -> 1(1) 0.3 X 2(6) -> 1(4) -1.2 2(9) -> 1(4) 1.2 1 2(8) -> 1(1) 0.0 X 2(9) -> 1(5) 0.2 1 2(9) -> 1(6) 0.1 1 2(9) -> 1(7) -0.2 2(8) -> 1(1) 1.3 X 2(7) -> 1(2) -0.4 2(8) -> 1(2) 1.1 X 2(7) -> 1(1) -0.4 2(8) -> 1(4) 0.5 1 2(7) -> 1(1) -1.0 2(8) -> 1(5) -0.2 2(7) -> 1(1) 1.0 X 2(7) -> 1(2) 0.8 X 2(7) -> 1(4) 0.2 1 2(7) -> 1(5) -0.8 2(6) -> 1(1) 0.3 X 2(6) -> 1(2) 0.1 X 2(6) -> 1(4) -0.5 2(5) -> 1(1) -0.1 1(2), 2.6, 2(9) -> 1(1) 2.1 X 1 2(8) -> 1(3) 0.6 X 2(7) -> 1(4) -1.7 2(8) -> 1(4) 0.1 X 2(8) -> 1(5) -0.9 2(7) -> 1(3) 0.3 X 2(7) -> 1(4) -0.2 2(6) -> 1(3) -0.4 2(9) -> 1(3) 1.8 1 2(8) -> 1(1) 0.6 X 2(7) -> 1(4) -1.7 2(8) -> 1(4) -0.2 2(7) -> 1(1) 0.3 X 2(7) -> 1(4) -0.5 2(6) -> 1(1) -0.4 2(9) -> 1(4) 1.3 1 2(8) -> 1(1) 0.1 X 2(7) -> 1(3) -1.7 2(9) -> 1(5) 0.3 1 2(9) -> 1(6) 0.2 1 2(9) -> 1(7) -0.1 2(8) -> 1(1) 1.4 X 2(7) -> 1(3) -0.4 2(8) -> 1(3) 1.1 1 2(7) -> 1(1) -0.4 2(8) -> 1(4) 0.6 1 2(7) -> 1(1) -0.9 2(8) -> 1(5) -0.1 2(7) -> 1(1) 1.1 X 2(7) -> 1(3) 0.8 1 2(7) -> 1(4) 0.3 1 2(7) -> 1(5) -0.7

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2(6) -> 1(1) 0.4 X 2(6) -> 1(3) 0.1 1 2(6) -> 1(4) -0.4 2(5) -> 1(1) 0.0 X 1(1), 2.8, 2(9) -> 1(2) 2.1 1+1 2(8) -> 1(3) 0.6 X 2(7) -> 1(4) -1.7 2(8) -> 1(4) 0.1 X 2(8) -> 1(5) -0.9 2(7) -> 1(3) 0.3 X 2(7) -> 1(4) -0.2 2(6) -> 1(3) -0.4 2(9) -> 1(3) 2.0 1 2(8) -> 1(2) 0.6 1 2(7) -> 1(4) -1.7 2(8) -> 1(4) 0.0 1 2(7) -> 1(2) 0.3 1 2(7) -> 1(4) -0.3 2(6) -> 1(2) -0.4 2(9) -> 1(4) 1.5 1 2(8) -> 1(2) 0.1 1 2(7) -> 1(3) -1.7 2(9) -> 1(5) 0.5 1 2(9) -> 1(6) 0.4 1 2(9) -> 1(7) 0.1 1 2(9) -> 1(8) -0.2 2(8) -> 1(2) 1.4 1 2(7) -> 1(3) -0.4 2(8) -> 1(3) 1.3 1 2(7) -> 1(2) -0.4 2(8) -> 1(4) 0.8 1 2(8) -> 1(5) -0.2 2(7) -> 1(2) 1.1 1 2(7) -> 1(3) 1.0 1 2(7) -> 1(4) 0.5 1 2(7) -> 1(5) -0.5 2(6) -> 1(2) 0.4 1 2(6) -> 1(3) 0.3 1 2(6) -> 1(4) -0.2 2(5) -> 1(2) 0.0 1 Thus one-sided probability = 42/184756 = .0002373 and 2 sided probability = .0004546

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Below is the reference table of values in the 2 groups, together with the effect on T of switching data points between the 2 groups: Group 1 1 148.10 2 148.30 3 148.40 4 148.90 5 149.90 6 150.00 7 150.30 8 150.60 9 152.50 10 153.20 Group 2 effect on T of switching between groups 1 and 2 1 137.50 2 140.60 3 143.80 4 144.10 -4 5 145.50 -2.6 -2.8 6 145.90 -2.2 -2.4 -2.5 -3 7 146.60 -1.5 -1.7 -1.8 -2.3 -3.3 8 146.90 -1.2 -1.4 -1.5 -2 -3 9 147.60 -0.5 -0.7 -0.8 -1.3 -2.3 -2.4 -2.7 -3 10 150.90 2.8 2.6 2.5 2.0 1.0 0.9 0.6 0.3 1 2 3 4 5 6 7 8 ______________________________________________________________________

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6.5 DUNNETT TEST Dunnett, CW, in 2 papers: "A Multiple comparison procedure for comparing several treatments with a control"3, and "New Tables for Multiple Comparisons with a Control"4, described a technique for calculating probabilities when performing multiple comparisons against the same control group. We have already described above in section 2 the Ahner Passing procedure for calculating these probabilities and compared them against the tables in Dunnett's papers. Appendix 4B gives the results of applying the Dunnett test to the test statistics for Sodium at 6 months. Note that the T-test statistic should be based upon using the combined variance from all groups - the Roelee standard analysis. From those results we can look up the test statistic against the tables in Dunnett's second paper for comparison: Sodium at 6 months, males: Group 2 3 4 T statistic: 3.6087 3.2180 5.0792 degrees of freedom: 36 P from Dunnett tables: <0.01 <0.01 <0.01 (2-sided, 3 comparison groups, df=40) 2.44 for p<0.05, 3.09 for p<0.01 Sodium at 6 months, females: Group 2 3 4 T statistic: 2.0117 0.4611 0.8674 degrees of freedom: 35 P from Dunnett tables: N.S. N.S. N.S. (2-sided, 3 comparison groups, df=40) 2.44 for p<0.05, 3.09 for p<0.01 To get some better tables for comparison, the Ahner Passing procedure was run to create Dunnett tables for p=0.005, .002 and .001 for degrees of freedom as in Appendix 1A but including the case where degrees of freedom = 35. These are presented in Appendix 4E. From these it can be seen that: Sodium at 6 months, males: Group 2 3 4 T statistic: 3.6087 3.2180 5.0792 degrees of freedom: 36 P from Dunnett tables: <0.005 <0.01 <0.001 (2-sided, 3 comparison groups, df=35) 2.44 for p<0.05, 3.09 for p<0.01 3.381 for p<0.005, 3.714 for p<0.002, 3.916 for p<0.001 In 1991 Dunnett published a follow-up paper12 which described a step-down version of this procedure, similar to the Bonferroni procedure of Holm given above{HOCKBE1988}. Basically, the simple Student T test statisticsfor each pairwise comparisons (using the pooled standard deviation) are ordered, and then are tested starting with the highest value and continuing on to the next highest, at each stage using only the remaining groups to estimate the correlation structure and basing the probabilities on only the number of hypotheses yet to be tested. As per usual, we insist that the probabilities generated cannot be smaller than those

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of the previous step. This has been implemented in RoeLee by use of a “/STEPWISE” qualifier. Note that this can also be used in the Steel procedure for multiply adjusting Wilcoxon probabilities and for the Ahner-Passing procedure for multiply adjusting chi-squared probabilities. ______________________________________________________________________

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6.6 LEVENE TEST Howard Levene, in his paper "Robust Tests for Equality of Variances" 13, put forward an alternative procedure to the Bartlett method for testing differences in variances between groups. This method was based on taking the absolute differences between the values of each group from their group mean and then doing an analysis of variance between the transformed data. We have implemented this procedure in the same way except that we do a non-parametric analysis of variance on the transformed data, essentially using the Kruskal-Wallis test. To test the procedure, we have written a command file, TLEVENE.CMD, that does the required transformation using standard RoeLee commands and then does a standard Kruskal-Wallis analysis on the resulting values. These are then compared to the values in Appendix 4B to check that the resulting probabilities are correct. Note, where it has been possible to calculate the probabilities exactly (where the numbers in the two groups being compared is not too large) these probabilities have been used rather than the asymptotic probabilities. The results from running the TLEVENE.CMD command file are given in Appendix 4G and cross- checking the results shows complete agreement in the numbers from the tables for males, females and males+females. In order to aid comparisons with other computer systems we have allowed for the possibility of performing a parametric analysis in place of the non-parametric analysis. Also, when performing a parametric analysis we could use the square of the differences instead of taking the absolute differences. Users can make using of these options by using system message S0006 and setting: Column 21 <=1 for Absolute differences, 2 for squared differences, Column 22 <=1 for Krusal-Wallis, 2 for F-test ______________________________________________________________________

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6.7 BONFERRONI ADJUSTMENTS The four different types of Bonferroni adjustment have been described above in section 3. These have been applied to the results from the t-tests in Appendix 4B and marked as B1, B2, B3 and B4. Now for Sodium at 6 months, males: Input probabilities : 0.000928, 0.002731, 0.000012 B1: multiply by 3 : 0.002784, 0.008193, 0.000036 adjust to levels : 0.01 , 0.01 , 0.000036 B2: order probs: .000012, .000928, .002731 H(1), reject when P(1) < α/3, as P(1) <0.000333 adjust P(1) to .001 H(2), reject when P(2) < α/2, and P(1) < α/3 as 0.01/2 > P(2) > .001/2, adjust P(2) to 0.01 H(3), reject when P(3) < α, P(2) < α/2, P(1) < a/3 now, P(3) <0.001, but 0.01/2 > P(2) > .001/2 thus adjust P(3) to 0.01 B3: order probs : .000012, .000928, .002731 let α=.05, then J = [i s.t. P(3-i+k) > k(0.05)/i, k=1,i let i=1, k=1, then P(3) < 0.05 i=2, k=1, P(2) < 0.025, k=2, P(3) < 0.05 i=3, k=1, P(1) < 0.01666 k=2, P(2) < 0.03333 k=3, P(3) < 0.05 J is empty so reject all Hi at level of 0.05 let α=.01, then let i=1, k=1, then P(3) < 0.01 i=2, k=1, P(2) < 0.005, k=2, P(3) < 0.01 i=3, k=1, P(1) < 0.00333 k=2, P(2) < 0.00666 k=3, P(3) > 0.01 J is empty so reject all Hi at level of 0.01

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let α=.001, then let i=1, k=1, then P(3) > 0.001, hence 1 belongs to J i=2, k=1, P(2) > 0.0005, k=2, P(3) > 0.001 , hence 2 belongs to J i=3, k=1, P(1) < 0.00033 k=2, P(2) > 0.00066 k=3, P(3) > 0.001 max J = 2 Hence reject all Hi where Pi <0.0005 here reject only H3 at the level of 0.001 Hence reject H1 and H2 at the level of 0.01, H3 at the level of 0.001 B4: order probs : .002731, .000928, .000012 H(1), accept if P(1) > α for α=.05, P(1)<α, so reject all at this level for α=.01, P(1)<α, so reject all at this level for α=.001,P(1)>α, so accept at this level H(2), accept if P(2) > α if α=.001, α/2=.0005, so accept at this level H(3), accept if P(3) >α/3 = .000333 if α=.001, reject Thus, reject H1 and H2 at p<.01, H3 at p<.001 Sodium at 6 months, females, were all non-significant before adjustment. Sodium at 6 months, males+females: Input probabilities : 0.000743, 0.037162, 0.041562 B1: multiply by 3 : 0.002229, 0.111486, 0.123686 adjust to levels: 0.01 , 1.0 , 1.0 B2: order probs: : .000743, .037162, .041562 H(1), reject when P(1) < α/3, as .00333 > P(1) > 0.000333 adjust P(1) to .01 H(2), reject when P(2) < α/2, and P(1) < α/3 as 0.1/2 > P(2) > .05/2, adjust P(2) to 0.1 H(3), reject when P(3) < α, P(2) < α/2, P(1) < α/3 now, P(3) <0.05, but 0.1/2 > P(2) > .05/2 thus adjust P(3) to 0.1 Thus, reject H1 at P<0.01 and H2 and H3 at p<0.1

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B3: order probs: : .000743, .037162, .041562 J = [i s.t. P(3-i+k) > k(0.05)/i, k=1,i let α=.05, let i=1, k=1, then P(3) < 0.05 i=2, k=1, P(2) > 0.025, k=2, P(3) < 0.05 i=3, k=1, P(1) < 0.01666 k=2, P(2) > 0.03333 k=3, P(3) < 0.05 J is empty so reject all Hi at level of 0.05 let α=.01, then let i=1, k=1, then P(3) > 0.01 hence, J = [1 i=2, k=1, P(2) > 0.005, k=2, P(3) > 0.01 hence, J = [1,2 i=3, k=1, P(1) < 0.00333 k=2, P(2) > 0.00666 k=3, P(3) > 0.01 J is empty so reject all Hi at level of 0.01 max J = 2 Hence reject all Hi where Pi <0.005 here reject only H3 at the level of 0.01 let α=.001, then let i=1, k=1, then P(3) > 0.001, hence 1 belongs to J i=2, k=1, P(2) > 0.0005, k=2, P(3) > 0.001 , hence 2 belongs to J i=3, k=1, P(1) > 0.00033 k=2, P(2) > 0.00066 k=3, P(3) > 0.001 max J = 3 Hence reject all Pi where Pi <0.000333 here reject no hypothesis at the level of 0.001 Hence reject H1 and H2 at the level of 0.05, H3 at the level of 0.01

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B4: order probs: : .041562, .037162, .000743 H(1), accept if P(1) > α for a=.05, P(1) <α, so reject all hypotheses at this level for α=.01, P(1) >α, so accept at this level H(2), accept if P(2) > α/2 = 0.005, so accept H(3), accept if P(3) > α/3 = 0.0033, so reject at this level if α=.001, P(1) >α, so accept at this level H(2), accept if P(2) > α/2 = 0.0005, so accept H(3), accept if P(3) > α/3 = 0.00033, so accept Thus, reject H2 and H3 at p<.05 and reject H1 at p<.01 ______________________________________________________________________

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6.8 LÜDIN PROCEDURE The Lüdin procedure has been explained above in section 4. The results in the tables in Appendix 4B should enable us to confirm that the procedure is working correctly in this case. Thus for Sodium at 6 months, males, the first F value should be that from the trend test over all groups, 14.413788. Its probability was .000543 and as that was less than 0.05, this probability was assigned to the top dose group, group 4. Group 4 was then removed from the analysis and the trend test re-done. At the bottom of the page, the value for the trend ignoring group 4 was found to be 4.845035, p=0.036457. As this value was still less than 0.05, these values were assigned to group 3 and the test re-done with only groups 1 and 2 left. Page 2 of table 2 reveals an F value of 15.097348 with p=0.0010804 which was then finally assigned to group 2. With the Lüdin procedure set at 0.001, the top dose was still significant, but the probability for group 3 was greater than 0.001. The procedure stopped at that point with an analysis of the 3 remaining groups - the figures agreeing with those from the 3 group analysis. Similar cross-checking of the other tables confirmed that the procedure was being handled as expected. ______________________________________________________________________

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7. NON-PARAMETRIC STATISTICS Non-parametric statistics are organised around the keyword KWALL and the routine ndescb in module NONP.FOR and the module KWALL.FOR. The command file, TKWALL.CMD given in Appendix 5A, has been written to produce test results from the RoeLee Worked Example based on the same data as shown in section 6. The results from running the command file are given in Appendix 5B. ______________________________________________________________________ 7.1 DESCRIPTIVE STATISTICS The following descriptive statistics are calculated in this form of analysis: Note we include the RoeLee descriptors for each statistic used. STAT_ID Statistic Description RoeLee 1 N number of observations

The number of non-missing observations in each group and optionally the total over groups is given.

5 Min Minimum observation value 6 Max Maximum observation value 7 Q99 99% Quantile 8 Q95 95% Quantile 9 Q75 75% Quantile 10 Median 50% Quantile - Median 11 Q25 25% Quantile 12 Q5 5% Quantile 13 Q1 1% Quantile

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note quantiles are defined by use of the empirical distribution function with averaging, that is let y = (xj + xj+1)/2 if g=0 y = xj+1 if g>0 where np = j+g p = t/100 (t th percentile) n = number of nonmissing values g = fractional part on np j = the jth animal in the ordered data 18 QRange Quartile Range Qrange = Q(0.75) - Q(0.25) 19 Miss Number of missing values 1) missing on the factor of interest 2) belong to a factor level that has been marked as required to be ignored 3) belonging to animals that have been declared by users to be excluded from the analysis 4) belong to a missing partition, stratum, time or grouped time level 5) have a covariate that has missing values 6) have missing values on the variable of interest The missing values printed are those found after removing all values excluded by possibilities 1 to 5.

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The results for Sodium at 6 months, males, are given in Appendix 5B, Table 1. Now for Sodium at 6 months, Males: Group 1 Values 1 148.10 2 148.30 3 148.40 4 148.90 5 149.90 6 150.00 7 150.30 8 150.60 9 152.50 10 153.20 B.1 n = 10 B.5 Min = 148.1 B.6 Max = 153.2 B.10 Median (149.9+150)/2 = 149.95 B.7 Q99, np = 9 + 0.9, y=153.2 B.8 Q95, np = 9 + 0.5, y=153.2 B.9 Q75, np = 7 + 0.5, y=150.6 B.11 Q25, np = 2 + 0.5, y=148.4 B.12 Q5 , np = 0 + 0.5, y=148.1 B.13 Q1 , np = 0 + 0.1, y=148.1 B.18 Qrange = Q75-Q25 = 2.2 B.19 Nmiss = 0 Group 2 Values 1 137.50 2 140.60 3 143.80 4 144.10 5 145.50 6 145.90 7 146.60 8 146.90 9 147.60 10 150.90 B.1 n = 10 B.5 Min = 137.5 B.6 Max = 150.9

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B.10 Median (145.5+145.9)/2 = 145.7 B.7 Q99, np = 9 + 0.9, y=150.9 B.8 Q95, np = 9 + 0.5, y=150.9 B.9 Q75, np = 7 + 0.5, y=146.9 B.11 Q25, np = 2 + 0.5, y=143.8 B.12 Q5 , np = 0 + 0.5, y=137.5 B.13 Q1 , np = 0 + 0.1, y=137.5 B.18 Qrange = Q75-Q25 = 3.1 B.19 Nmiss = 0 Group 3 Values 1 138.00 2 139.80 3 144.50 4 145.30 5 145.80 6 146.70 7 147.90 8 148.50 9 148.50 10 149.90 B.1 n = 10 B.5 Min = 138.0 B.6 Max = 149.9 B.10 Median (145.8+146.7)/2 = 146.25 B.7 Q99, np = 9 + 0.9, y=149.9 B.8 Q95, np = 9 + 0.5, y=149.9 B.9 Q75, np = 7 + 0.5, y=148.5 B.11 Q25, np = 2 + 0.5, y=144.5 B.12 Q5 , np = 0 + 0.5, y=138.0 B.13 Q1 , np = 0 + 0.1, y=138.0 B.18 Qrange = Q75-Q25 = 4.0 B.19 Nmiss = 0 Group 4 Values 1 135.70 2 141.80 3 142.40 4 142.90 5 143.60 6 143.60 7 143.80 8 144.40 9 145.10

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10 145.40 B.1 n = 10 B.5 Min = 135.7 B.6 Max = 145.4 B.10 Median = 143.6 B.7 Q99, np = 9 + 0.9, y=145.4 B.8 Q95, np = 9 + 0.5, y=145.4 B.9 Q75, np = 7 + 0.5, y=144.4 B.11 Q25, np = 2 + 0.5, y=142.4 B.12 Q5 , np = 0 + 0.5, y=135.7 B.13 Q1 , np = 0 + 0.1, y=135.7 B.18 Qrange = Q75-Q25 = 2.0 B.19 Nmiss = 0 While for Sodium at 6 months, males + females: Group 1 Values 1 144.0 2 144.5 3 145.1 4 145.3 5 145.3 6 145.7 7 146.3 8 147.2 9 147.4 10 148.1 11 148.3 12 148.4 13 148.9 14 149.9 15 150.0 16 150.3 17 150.6 18 152.5 19 153.2 B.1 n = 19 B.5 Min = 144.0 B.6 Max = 153.2 B.10 Median = 148.1 B.7 Q99, np =18 + 0.81, y=153.2 B.8 Q95, np =18 + 0.05, y=153.2 B.9 Q75, np =14 + 0.25, y=150.0 B.11 Q25, np = 4 + 0.75, y=145.3 B.12 Q5 , np = 0 + 0.95, y=144.0

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B.13 Q1 , np = 0 + 0.19, y=144.0 B.18 Qrange = Q75-Q25 = 4.7 B.19 Nmiss = 1 Group 2 Values 1 127.4 2 137.5 3 138.0 4 140.6 5 140.9 6 141.5 7 141.8 8 142.6 9 142.9 10 143.8 11 144.1 12 145.4 13 145.5 14 145.9 15 146.4 16 146.6 17 146.9 18 147.6 19 147.9 20 150.9 B.1 n = 20 B.5 Min = 127.4 B.6 Max = 150.9 B.10 Median = 143.95 B.7 Q99, np =19 + 0.8, y=150.9 B.8 Q95, np =19 + 0 , y=149.4 B.9 Q75, np =15 + 0 , y=146.5 B.11 Q25, np = 5 + 0 , y=141.2 B.12 Q5 , np = 1 + 0 , y=132.45 B.13 Q1 , np = 0 + 0.2, y=127.4 B.18 Qrange = Q75-Q25 = 5.3 B.19 Nmiss = 0

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Group 3 Values 1 132.1 2 134.4 3 138.0 4 139.8 5 142.2 6 144.5 7 145.3 8 145.8 9 146.3 10 146.7 11 147.1 12 147.9 13 148.1 14 148.1 15 148.5 16 148.5 17 148.9 18 149.5 19 149.9 20 150.2 B.1 n = 20 B.5 Min = 132.1 B.6 Max = 150.2 B.10 Median = 146.9 B.7 Q99, np =19 + 0.8, y=150.2 B.8 Q95, np =19 + 0 , y=150.05 B.9 Q75, np =15 + 0 , y=148.5 B.11 Q25, np = 5 + 0 , y=143.35 B.12 Q5 , np = 1 + 0 , y=133.25 B.13 Q1 , np = 0 + 0.2, y=132.1 B.18 Qrange = Q75-Q25 = 5.15 B.19 Nmiss = 0 Group 4 Values 1 135.7 2 141.8 3 142.4 4 142.9 5 143.6 6 143.6 7 143.8 8 144.4 9 144.4

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10 145.1 11 145.4 12 145.6 13 145.8 14 146.0 15 147.4 16 148.3 17 148.5 18 149.3 19 149.4 20 149.7 B.1 n = 20 B.5 Min = 135.7 B.6 Max = 149.7 B.10 Median = 145.25 B.7 Q99, np =19 + 0.8, y=149.7 B.8 Q95, np =19 + 0 , y=149.55 B.9 Q75, np =15 + 0 , y=147.85 B.11 Q25, np = 5 + 0 , y=143.6 B.12 Q5 , np = 1 + 0 , y=138.75 B.13 Q1 , np = 0 + 0.2, y=135.7 B.18 Qrange = Q75-Q25 = 4.25 B.19 Nmiss = 0 ______________________________________________________________________

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7.2 WILCOXON TEST As explained in detail in Test of Statistics, section 2, RoeLee treats the Wilcoxon test as a special case of the Kruskal-Wallis test. Note that the exact probability for 2 group comparisons can be calculated when the numbers of cases was not too large by using the same technique as used in the Fisher Exact trend test, as it was noted by PNL that there was a 1-1 correspondence between the two problems: In 2 group comparisons, Σ Ri, the sum of the ranks for the control group is a sufficient statistic. Thus we can take the rankings of the joint control and comparison groups as equivalent to the trend coefficients in the exact trend situation, with the trend score now equivalent to the sum of ranks for the control group. The number of control animals having each rank represents the number of affected animals for different trend coefficients, and the number of animals in the comparison group having each rank becomes the number of not affected animals for different trend coefficients. In practice, we use twice the rank as the trend coefficient, so that the result is always integral, even when ties occur. For example:

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Sodium at 6 months, males, Joint rank order: Group 1 v 2 Group 1 v 3 1 137.50 2 1 138.00 3 2 140.60 2 2 139.80 3 3 143.80 2 3 144.50 3 4 144.10 2 4 145.30 3 5 145.50 2 5 145.80 3 6 145.90 2 6 146.70 3 7 146.60 2 7 147.90 3 8 146.90 2 8 148.10 1 9 147.60 2 9 148.30 1 10 148.10 1 10 148.40 1 11 148.30 1 11.5 148.50 3 12 148.40 1 11.5 148.50 3 13 148.90 1 13 148.90 1 14 149.90 1 14.5 149.90 1 15 150.00 1 14.5 149.90 3 16 150.30 1 16 150.00 1 17 150.60 1 17 150.30 1 18 150.90 2 18 150.60 1 19 152.50 1 19 152.50 1 20 153.20 1 20 153.20 1 Equivalent exact trend problem: Group 1 v 2 Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Trend Coeff. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 no. affected 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 no. not-affected 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 Group 1 v 3 Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Trend Coeff. 2 4 6 8 10 12 14 16 18 20 23 26 29 32 34 36 38 40 no. affected 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 no. not-affected 1 1 1 1 1 1 1 0 0 0 2 0 1 0 0 0 0 0 For details of solving the exact trend problem, users are referred to Test of Statistics, section 7. The routine used, Extrnd, is given in Appendix 4C. ______________________________________________________________________

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7.3 KRUSKAL-WALLIS TEST The Kruskal-Wallis test is a standard test in RoeLee and users are referred to Test of Statistics, section 2, for full details. ______________________________________________________________________ 7.4 STEEL TEST In his paper, "A Multiple Comparison Rank Sum Test: Treatment versus control" 5, Steel put forward a solution to the problem of multiple comparisons versus one control group for rank tests. This was equivalent to the work Dunnett had done for the Student t-test, and an approximate solution was found in terms of Dunnett's tables. As explained above in section 2, Steel used Dunnett's original tables in his paper, which were fairly inaccurate for large numbers of comparison groups, and we shall be using the Ahner-Passing procedure for calculating these probabilities. Similarly to section 6.5, we have used the Ahner-Passing procedure to calculate tables of critical values for the Steel test for values 0.05, 0.01, 0.005, 0.002 and 0.001 and these are shown in Appendix 5C. Using these tables we can compare the probabilities in Appendix 5B for the Steel test to these critical values. Note that the Steel probabilities are approximately 3 times the uncorrected probabilities - which can also be seen when examining the Dunnett probabilities in Appendix 4B. For the Steel test, the test statistic should be the square root of the value shown against "ChiSq". Sodium at 6 months, males: Group 2 3 4 Test statistic: 3.175 2.988 3.781 P values: P<0.005 P<0.01 P<0.0005 Critical values from Steel tables, 2-sided, 3 comparison groups: .05=2.349, .01=2.915, .005=3.13, .002=3.394, .001=3.581, .0005=3.66 ______________________________________________________________________

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7.5 JONCKHEERE TEST Jonckheere, in his paper "A Distribution-free k-Sample test against ordered Alternatives", 14, 41, introduced a trend test based on the rank order of the trend coefficients, rather than the actual values of the trend coefficients. (RoeLee already has a rank test using the actual values of the trend coefficients, and this is described in Test of Statistics, section 2.) In his paper, Jonckheere shows that the distribution of his test statistic can be calculated from a probability generating function, can be approximated to from the Student t distribution, and finally, where there are large numbers it can be approximated to by a normal distribution. We have developed programs to get the probability from the probability generating function and have used it to generate the probabilities in Jonckheere's paper, with comparison probabilities from using the Normal and the Student t approximations. The results are given in Appendix 5D, with the module itself given in Appendix 5E. It seems clear that the figures are the same as generated by Jonckheere, that for small numbers the exact figures are best, but that the Student t approximation is very good. Thus, we have decided to use the exact probabilities when the number of possible values of the test statistic is less than 300, otherwise we will use the values for the Student t. Now, we still have to calculate the Jonckheere statistic itself: k-1 k k-1 k S = 2 Σ Σ pij - Σ Σ mi mj i=1 j=1+i i=1 j=1+i where Piαi jαj= 1 if Xiαi < Xjαj 0 if Xiαi > Xjαj 1/2 if Xiαi = Xjαj mi mj

and Pij = Σ Σ Piαijαj αi=1 αj=1 k = number of groups mi = number of animals in group i, i=1, .., k αi = αith animal in group i

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For Sodium at 6 months, males Combined rank order: Group 1 135.70 4 2 137.50 2 3 138.00 3 4 139.80 3 5 140.60 2 6 141.80 4 7 142.40 4 8 142.90 4 9.5 143.60 4 9.5 143.60 4 11.5 143.80 4 11.5 143.80 2 13 144.10 2 14 144.40 4 15 144.50 3 16 145.10 4 17 145.30 3 18 145.40 4 19 145.50 2 20 145.80 3 21 145.90 2 22 146.60 2 23 146.70 3 24 146.90 2 25 147.60 2 26 147.90 3 27 148.10 1 28 148.30 1 29 148.40 1 30.5 148.50 3 30.5 148.50 3 32 148.90 1 33.5 149.90 1 33.5 149.90 3 35 150.00 1 36 150.30 1 37 150.60 1 38 150.90 2 39 152.50 1 40 153.20 1

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10 10 P12 = Σ Σ P1i 2j = 8, P21 = 100 – P12 = 92 i=1 j=1 P13 = 3+3+3+ 1 + 0.5 = 10.5, P31 = 89.5 P14 = 0, P41 = 100 P23 = 0 +4+4 +5+5 +6 +8+8+8 +10 = 58, P32 = 42 P24 = 6*0 + 3 +3.5 + 2*9 = 24.5 , P42 = 75.5 P34 = 6*0 + 1 +2 +2*9 = 21, P43 = 79 S= 2*(P12 + P13 + P14 + P23 + P24 + P34) - (300+200+100) = 2*(8 + 10.5 + 0 + 58 + 24.5 + 21) - 600 = 244 - 600 = -356 For the t-test we require tν = S1 √ [ ν / [(ν+1)µ2 - S12] where, ν = degrees of freedom = -3( 2 + γ2)/γ2 S1 = S-1 if S >0 S+1 if S <0 k γ2 = -(36/25)[n3(6n2+15n+10) - Σ mr

3 (6mr2+15mr +10) ]

r=1 ______________________________________ k [ n2(2n+3) - Σ mr

2(2mr +3) ] 2 r=1 k µ2 = (1/18) [n2(2n+3) - Σ mr

2(2mr +3) ] r=1 k = number of groups mr = number of animals in group r n = total number of animals

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Here, k=4, mr=10, r=1,...,4, n=40 µ2 = (1/18)(132800- 9200) = 6866.6667 γ2 =- (36/25)[64000(9600+600+10) - 4x1000(600+150+10 ) ]/ (18*6866.6667)2 =- (1/(9x25))[64000x10210 - 4000x760]/6866.6667 2 =- (1/(9x25))x10000x65040/6866.6667 2 = -0.061306437 ν = -3(2+ γ2)/ γ2 = 94.86900464 tν = -355 * √[ 94.86900369/[95.86900369 µ2 - 3552 ] ] = 4.73938824 Results given in Appendix 5B Table 1 are of tν

2 = 22.46180089

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For Sodium at 6 months, females: 1 37 2 127.4 2 52 3 132.1 3 51 3 134.4 4 35 2 138.0 5 38 2 140.9 6 33 2 141.5 7 34 2 141.8 8 53 3 142.2 9 39 2 142.6 10 36 2 142.9 11 20 1 144.0 12 75 4 144.4 13 16 1 144.5 14 13 1 145.1 15.5 11 1 145.3 15.5 19 1 145.3 17 32 2 145.4 18 79 4 145.6 19 15 1 145.7 20 78 4 145.8 21 80 4 146.0 22.5 17 1 146.3 22.5 58 3 146.3 24 40 2 146.4 25 55 3 147.1 26 18 1 147.2 27.5 73 4 147.4 27.5 12 1 147.4 29 31 2 147.9 30.5 59 3 148.1 30.5 60 3 148.1 32 77 4 148.3 33 72 4 148.5 34 54 3 148.9 35 71 4 149.3 36 74 4 149.4 37 56 3 149.5 38 76 4 149.7 39 57 3 150.2 P12 = 2*1 +2*2 +5*3 = 21 P13 = 2*5 + 6.5 + 6*7 = 58.5 P14 = 5.5 + 2*6 +8 +4*9 +10 = 71.5 P23 = 5 + 6 + 3*7 + 4*8 +10 = 74 P24 = 5 + 6 + 9 + 7*10 = 90 P34 = 0 + 1 + 3 + 2*5 +2*6 +3*10 = 56

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S = 2*(371) - (3*90 + 2*100 + 100) = 172 Here, k=4, m1=9, mr=10, r=2, 3, 4, n=39 where, ν = degrees of freedom = -3( 2 + γ2)/γ2 S1 = S-1 if S >0 S+1 if S <0 k γ2 = -(36/25)[n3 (6n2+15n+10) - Σ mr

3(6mr2+15mr +10) ]

r=1 __________________________________ k [n2(2n+3) - Σ mr

2(2mr +3)2 ] r=1 k µ2 = (1/18) [n2(2n+3) - Σ mr

2(2mr +3) ] r=1 µ2 = (1/18)(123201 - 1701 -3x2300) =114600/18 = 6366.6667 γ2 =- (1/(9*25))[59319(9721) - 729(631) - 3000(760) ]/ 6366.66672

=- (1/(9*25))[573900000 ]/ 6366.66672

=- 0.062925905 ν = 3(2-0.062925905)/0.062925905 = 92.35023623 tν = 2.18603319 Results given in Appendix 5B Table 2 are of tν

2 = 4.778741108 ______________________________________________________________________

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7.6 BONFERRONI ADJUSTMENTS These adjustments have been gone through in detail in the sections 3. and 6.7 above. Here we mark the adjusted probabilities by KB1 to KB4 representing the four types of adjustment allowed for. Note, the adjustment is for the asymptotic probabilities, unless these have been replaced by exact probabilities - currently this only occurs during the Lüdin procedure. ______________________________________________________________________ 7.7 LÜDIN PROCEDURE This procedure has been gone through in detail in sections 4. and 6.8 above. Here the results were cross-checked within the tables shown in Appendix 5B and the correct probabilities and statistics were seen in all cases. Note that where repeated Jonckheere tests were done, the test statistics were shown on one line. ______________________________________________________________________

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8. TEST OF 2xk TABLES Often it is required to test for differences between groups where the data measured is the number of affected animals out the the observed number of animals in each group. The two most common tests used in these situations are the Fisher's Exact test and the Chi-squared tests, both of which are described in detail in Test of Statistics, sections 1 and 4. For some clients a slight alteration is needed to the Fisher's Exact test, and this is detailed in section 8.2. A new test, the Ahner-Passing test, was also required and this is detailed in section 8.4. We also have enabled Bonferroni adjustments and the Lüdin procedure for these types of test. The command files, TEXACT, given in Appendix 6A, and TCHI, given in Appendix 6C, have been written to produce test results from the RoeLee Worked Example based on the same data as shown in section 7. Note that in RoeLee we always use the Mantel-Haenszel form of the test statistic, that is we use a factor of (1/N) where N is the total number of cases. The classic Pearson form of the test statistic uses a factor of 1/(N-1). This form for the result can be requested by setting the system message S0006, column 20 to “1”. The results from running the command files are given in Appendix 6B and Appendix 6D. ______________________________________________________________________

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8.1 DESCRIPTIVE STATISTICS The following descriptive statistics are calculated in this form of analysis: Note we include the RoeLee descriptors for each statistic used. STAT_ID Statistic Description RoeLee 1 N number of observations The number of non-missing observations in each group and optionally the total over groups is given. 22 n number affected The number of animals having the condition, or the number of animals having at least a given level of a condition, the level being set by users. In Appendix 6B we have the results for Sodium at 6 months, where values greater than 146 defined positive values. Clearly from the ordered results shown in section 7.5 it can be seen: Sodium at 6 months Males Group 1 2 3 4 n 10 10 10 10 Naff (>146) 10 4 5 0 Females Group 1 2 3 4 n 9 10 10 10 Naff (>146) 3 2 7 6 Note the group 4 animal with value = 146.0 does not get counted as affected. ______________________________________________________________________

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8.2 FISHER EXACT TEST When calculating 2-tailed probabilities for the Fisher's Exact test there are two main solutions: 1. Take twice the miniumum probability 2. Take the sum of all probabilities less than or equal to the observed probability. There are arguments for both of these solutions, and the standard RoeLee default is to take the first solution. However, some clients require the second solution, and so an extra option has been put into RoeLee to allow users to choose between the two options. In Appendix 6B, the results are shown where levels of Sodium at 6 months greater than 146 define affected animals. In table 2, the results are identical because there are equal numbers in the control and the comparison groups. In Table 1, due to there being one missing female animal in group one, the results are different. The possible tables with their associated probabilities are shown below:

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Sodium at 6 months >146, females: Group 1 vs 2 Observed table (O): Group 1 2 T number affected 3 2 5 m1! m2! n1! n2! number not affected 6 8 14 P = -------------------- Total 9 10 19 a!b!c!d! (N-1)! = 5! 14! 9! 10! ---------------- 3! 2! 6! 8! 19! (O) P = 0.325077 Other possible tables: (1) 4 1 P = 0.108359 5 9 (2) 5 0 P = 0.018359 4 10 (3) 2 3 P = 0.371517 7 7 (4) 1 4 P = 0.162539 8 6 (5) 0 5 P = 0.021672 9 5 P(+) = O +3+4+5 = 0.880805 P(-) = O +1+2 = 0.4442719 P (2 minimum) = 0.8885438 P (ΣP<=.325077) = O +1+2+4+6 = 0.6284829

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Group 1 vs 3 Observed table (O): Group 1 2 T number affected 3 7 10 m1! m2! n1! n2! number not affected 6 3 9 P = ------------------- Total 9 10 19 a!b!c!d! N! = 10! 9! 9! 10! ---------------- 3! 7! 6! 3! 19! (O) P= 0.109117 Other possible tables: (1) 4 6 P = 0.286432 5 4 (2) 5 5 0.343718 4 5 (3) 6 4 0.190955 3 6 (4) 7 3 0.046764 2 7 (5) 8 2 0.00438416 1 8 (6) 9 1 0.00010825 0 9 (7) 2 8 0.0175366 7 2 (8) 1 9 0.000974258 8 1 (9) 0 10 0.000010825 9 0 P(+) = O +7+8+9 = 0.127639 P(-) = O +1+2+...+7 = 0.981478 P (2 minimum) = 0.255278 P (ΣP<=.109117) = O +4+...+9 = 0.178895

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Group 1 vs 4 Observed table (O): Group 1 2 T number affected 3 6 9 m1! m2! n1! n2! number not affected 6 4 10 P = ------------------- Total 9 10 19 a!b!c!d! (N-1)! = 9! 10! 9! 10! ---------------- 3! 6! 6! 4! 19! (O) P = 0.190954556 Other possible tables: (1) 2 7 P = 0.046764381 7 3 (2) 1 8 0.004384160731 8 2 (3) 0 9 0.0001082508822 9 1 (4) 4 5 0.343718201 5 5 (5) 5 4 0.286431834 4 6 (6) 6 3 0.109116889 3 7 (7) 7 2 0.017536642 2 8 (8) 8 1 0.0009742579402 1 9 (9) 9 0 0.00001082508822 0 10 P(+) = O +4+...+9 = O+0.757788648 = 0.948743204 P(-) = O +1+2+3 = 0.242211348 P (2 minimum) = 0.484422696 P (ΣP<=.0954772)= O +1+2+3+6+7+8+9 = 0.369849961 ______________________________________________________________________

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8.3 CHI-SQUARED TEST Full details of chi-squared tests are given in Test of Statistics, section 4. Results for Sodium at 6 months, taking values greater than 146 as defining affected animals are given in Appendix 6D. ______________________________________________________________________

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8.4 AHNER-PASSING TEST The Ahner-Passing test is a test of the proportion of affected animals in 2 groups, which by means of the Ahner-Passing procedure detailed in section 2 above, can be adjusted to allow for multiple comparisons verus a single control. Details of the Ahner-Passing test were taken from the same paper as the Ahner-Passing procedure. From that paper the test statistic for comparing group i with control group 1: Ti = Xi/ni – X1/n1 ------------------------------------------------------- √ [X./n. (1 - X./n.)] √ [ 1/n1 + 1/n1] √ [n./(n.-1)] where Xi = number affected in group i X. = total number affected over all groups ni = number affect in group i n. = total number observations over all groups the probability for Ti is then computed from the Ahner-Passing procedure with: f = degrees of freedom = infinity ci = 1 / √ [ (n1/ni) + 1 ] Now for Sodium at 6 months, males Group 1 2 3 4 T Xi 10 4 5 0 19 ni 10 10 10 10 40 Xi/ni 1 0.4 0.5 0 0.475 [1/n1+1/ni] 0.2 0.2 0.2 [X/n(1-X/n)] 0.249375 [n/(n-1)] 1.025641 Denom 0.0511538 Ti

2 7.0376047 4.8872224 19.548888 Ti 2.6528484 2.2107063 4.4214124

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While for Sodium at 6 months, females: Group 1 2 3 4 T Xi 3 2 7 6 18 ni 9 10 10 10 39 Xi/ni 0.3333333 0.2 0.7 0.6 0.4615384 [1/n1+1/ni] 0.2111111 0.2111111 0.21111111 [X/n(1-X/n)] 0.2485207 [n/(n-1)] 1.0263157 Denom 0.0538461 Ti

2 0.3301576 2.496827 1.320636 Ti 0.5745934 1.5801351 1.1491892 Which agree with Appendix 6B. ______________________________________________________________________

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8.5 TREND TESTS The trend tests used are those specified in sections 1 and 4 in Test of Statistics - the Fisher's Exact trend test and the Cochran-Armitage test for the Chi-squared situation. These are the tests which will be used to test for trends when the Lüdin prodecure is used. ______________________________________________________________________

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8.6 BONFERRONI ADJUSTMENTS These have already been discussed in sections 3 and 6.7 above. In the Fisher Exact test the 4 adjustments are marked as EB1 to EB4. Due to a lack of readily available flags in the SET CHI procedure, no Bonferroni adjustment is available in the Chi-squared test at this time. ______________________________________________________________________

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8.7 LÜDIN PROCEDURE This has already been discussed in sections 4 and 6.8 above. The figures can be cross-checked against the rest of the results given in Appendices 6B and 6B. Note that there is no heterogeniety test done when the Fisher-Exact test is performed. ______________________________________________________________________

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9. ANALYSIS OF COVARIANCE AND REGRESSION Many datasets require that covariates are taken into account, and it was decided to add, not just covariate analyses but also a more general approach which would allow for the multiple regression to be performed. The approach taken was to allow the system to deal with linear models where the error is assumed to be Normal, and to use the form of analysis specified by McCullagh and Nelder in their book, "Generalized Linear Models" 15. Essentially two forms of analysis were to be allowed for: 1) Users specify ONEWAY /COVAR <fieldlist>

In this form, the fields specified in <fieldlist> would be treated as straight covariates, and the analysis of variance done after taking account of those covariates. That is the model:

Yij = α + µi + βX + εij is used where Yij are the values for the jth animal on group i X are the covariates β are the coefficients for the covariates εij are i.i.d. ~ N(0,s2) µi are the means for each group α is a grand mean

The change in deviance for introducing the µi into the model is used as a test of heterogeneity, while the ratio of the µi to their computed standard errors is used for 2-way comparisons. The introduction of a term linear in dose is used to test for trend. The dose levels used are those set by the users via SET TREND.

In this form users are shown only the adjusted covariance probabilities. 2) Users specify ONEWAY /REGRESS <fieldlist>

In this form, a full analysis of deviance is done on the fields specified in the field list. That is:

Model 1: Yij = α + εij 2: Yij = α + β1x1 + εij ........ k: Yij = α + Σ β1x1 + εij

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followed by any interaction terms specified, where Xi*Xj asks for Xi, Xj and then the interaction of Xi and Xj Xi.Xj asks simply for the interaction term of Xi and Xj

In this form users are shown the deviance attached to each model, the degrees of freedom and the probability of bringing in the new term.

Also the coefficients, their standard errors and their probabilities are shown. Note that graded fields are treated as "factors" - that is each level is treated as independent and a separate coefficient used for each level. Two special fields have been made available to users: @fact - refers to the factor of interest @dose - uses the trend coefficients as a variable of interest To test these models, a test file was input into GLIM - the General Linear Modelling package developed by Nelder. This file is presented in Appendix 7C, with the results presented in Appendix 7D. A RoeLee command file, TACOVA.CMD given in Appendix 7A, was created and run and the results presented in Appendix 7B. It is clear, when cross checking these files, that RoeLee is generating essentially the same results as the GLIM program. Note that the Lüdin procedure can even be applied to the probabilities allowing for covariates. ______________________________________________________________________

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10. CONDITIONAL TESTS IN COMMAND FILES New facilities have been add to RoeLee allowing users to build combinations of tests within RoeLee command files. To do this it must be possible to pass probabilities out of routines back to command files. This is done in RoeLee by setting special parameters during the calls to analyses and allowing these to be accessed in command files by: B1 to Bn - the probability of 2-group comparison versus groups 1 to n BTOTAL - the probability of the heterogeneity test BTREND - the probability of the trend test. (Note that the F values corresponding to these values are stored in variables T1 to Tn, TTOTAL and TTREND.) In order to demonstrate and test this possibility, the command file TOWKW.CMD was created. This is presented in Appendix 8A with the results of running the command file given in Appendix 8B. In this command file a preliminary test is done to see if the variances can be assumed to be equal over all the groups. If so, a parametric one-way analysis of variance is done, otherwise a non-parametric analysis of variance is done. This test is done first using the Levene test to check the variances, then repeated using the Bartlett test. In practice it can be seen that for males both the Bartlett and the Levene test for overall variance was non-significant and so a parametric test was done. For females, both the Bartlett and the Levene test were significant and so non-parametric tests were done. For males and females combined, the Levene test was non-significant while the Bartlett test was significant, and so after the Levene test a parametric test was done while after the Bartlett test a non-parametric test was done. Note the result from the original variance testing can be hidden by turning off the printer before performing the test, resulting in a standard procedure that will just present the final parametric or non-parametric analysis. ______________________________________________________________________

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11. REFERENCES

1. Ahner C, Passing H. Berechnung der multivariaten t-Verteilung und simultane Verleiche gegen Kontrolle bei ungleichen Gruppenbesetzungen. EDV in Medizin und Biologie 1983;14:113-20.

2. Abramowitz M, Stegun IA, editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover Publications, Inc.; 1965, (Reprinted 1972 incorporating errata).

3. Dunnett CW. A multiple comparison procedure for comparing several treatments with

a control. Am Stat Assoc J 1955;Dec:1096-121.

4. Dunnett CW. New tables for multiple comparisons with a control. Biometrics 1964;Sep:482-91.

5. Steel RGD. A multiple comparison rank sum test: treatments versus control. Biometrics 1959;Dec:560-72.

6. Hochberg Y. A sharper Bonferroni procedure for multiple tests of significance. Biometrika 1988;75:800-2.

7. Hommel G. A comparison of two modified Bonferroni procedures. Biometrika 1989;76:624-5.

8. Hochberg Y, Benjamini Y. More powerful procedures for multiple significance testing. Stat Med 1990;9:811-8.

9. Lüdin E. A test procedure based on ranks for the statistical evaluation of toxicological studies. Arch Toxicol 1985;58:57-8.

10. Winer BJ. Two-factor experiment with repeated measures on one factor. In: Statistical principles in experimental design, 2nd edition. McGraw-Hill Book Company, Date unknown;518-39.

11. Welch BL. The generalization of student's' problem when several different population variances are involved. Biometrika 1947;34:28-44.

12. Dunnett CW, Tamhane AC. Step-down multiple tests for comparing treatments with a control in unbalanced one-way layouts. Stat Med 1991;10:939-47.

13. Levene H. Robust tests for equality of variances. In: Contributions to Probability and Statistics, Essays in Honor of Harold Hotelling. Stanford University Press, 1960;278-92. (Olkin I, MORE, editors. )

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15. McCullagh P, Nelder JA. Generalized linear models, Volume 37, 2nd edition. London: Chapman and Hall; 1989. (Cox DR, Hinkley DV, Rubin D, Silverman BW, editors. Monographs on statistics and applied probability.)

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Appendix 1A

Ahner-Passing Tables Dunnett's test, one sided, alpha = 0.01

Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 6.965 3 4.541 5.482 4 3.747 4.408 4.796 5 3.365 3.900 4.211 4.429 4.597 4.733 4.846 4.944 5.030 5.106 5.174 5.236 5.293 5.345 5.393 5.438 5.480 5.520 5.557 5.592 6 3.143 3.607 3.876 4.064 4.208 4.324 4.422 4.505 4.579 4.644 4.702 4.755 4.804 4.849 4.890 4.929 4.965 4.999 5.031 5.061 7 2.998 3.418 3.660 3.828 3.957 4.062 4.149 4.224 4.290 4.348 4.400 4.448 4.491 4.531 4.568 4.603 4.635 4.665 4.694 4.721 8 2.896 3.286 3.509 3.665 3.784 3.880 3.960 4.029 4.089 4.143 4.191 4.234 4.274 4.311 4.345 4.377 4.406 4.434 4.460 4.485 9 2.821 3.189 3.399 3.545 3.656 3.746 3.821 3.886 3.942 3.992 4.037 4.078 4.115 4.150 4.182 4.211 4.239 4.265 4.290 4.313 10 2.764 3.115 3.314 3.453 3.559 3.644 3.715 3.777 3.830 3.878 3.920 3.959 3.994 4.027 4.057 4.085 4.111 4.136 4.159 4.181 11 2.718 3.056 3.248 3.380 3.482 3.564 3.632 3.690 3.742 3.787 3.828 3.865 3.899 3.930 3.959 3.985 4.011 4.034 4.056 4.077 12 2.681 3.008 3.194 3.322 3.420 3.499 3.564 3.621 3.670 3.714 3.753 3.789 3.822 3.851 3.879 3.905 3.929 3.952 3.973 3.994 13 2.650 2.969 3.149 3.274 3.369 3.445 3.509 3.564 3.611 3.654 3.692 3.726 3.758 3.787 3.814 3.839 3.862 3.884 3.905 3.925 14 2.625 2.936 3.111 3.233 3.326 3.400 3.462 3.515 3.562 3.603 3.640 3.674 3.705 3.733 3.759 3.783 3.806 3.827 3.848 3.867 15 2.602 2.908 3.080 3.198 3.289 3.362 3.422 3.474 3.520 3.560 3.596 3.629 3.659 3.687 3.712 3.736 3.758 3.779 3.799 3.817 16 2.583 2.884 3.052 3.169 3.257 3.329 3.388 3.439 3.484 3.523 3.559 3.591 3.620 3.647 3.672 3.695 3.717 3.738 3.757 3.775 17 2.567 2.862 3.028 3.143 3.230 3.300 3.359 3.409 3.452 3.491 3.526 3.557 3.586 3.613 3.637 3.660 3.681 3.701 3.720 3.738 18 2.552 2.844 3.007 3.120 3.206 3.275 3.332 3.382 3.425 3.463 3.497 3.528 3.556 3.582 3.607 3.629 3.650 3.670 3.688 3.706 19 2.539 2.827 2.989 3.100 3.185 3.253 3.309 3.358 3.400 3.438 3.472 3.502 3.530 3.556 3.579 3.602 3.622 3.642 3.660 3.677 20 2.528 2.813 2.972 3.082 3.166 3.233 3.289 3.337 3.378 3.416 3.449 3.479 3.506 3.532 3.555 3.577 3.598 3.617 3.635 3.652 120 2.358 2.598 2.730 2.820 2.888 2.943 2.988 3.027 3.061 3.090 3.117 3.141 3.163 3.184 3.203 3.220 3.236 3.252 3.266 3.280 32000 2.326 2.558 2.685 2.772 2.837 2.889 2.933 2.970 3.002 3.031 3.056 3.080 3.101 3.120 3.138 3.155 3.170 3.185 3.199 3.211 -1 2.326 2.558 2.685 2.772 2.837 2.889 2.933 2.970 3.002 3.031 3.056 3.079 3.100 3.120 3.138 3.154 3.170 3.185 3.198 3.211

Dunnett's test, one sided, alpha = 0.05

Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 2.920 3 2.353 2.938 4 2.132 2.610 2.885 5 2.015 2.440 2.681 2.848 2.976 3.078 3.163 3.236 3.300 3.356 3.407 3.453 3.494 3.533 3.569 3.602 3.633 3.662 3.689 3.715 6 1.943 2.337 2.558 2.711 2.827 2.920 2.998 3.064 3.122 3.174 3.220 3.261 3.299 3.334 3.367 3.397 3.425 3.451 3.476 3.499 7 1.895 2.267 2.476 2.619 2.728 2.815 2.888 2.950 3.004 3.052 3.095 3.134 3.169 3.202 3.232 3.260 3.286 3.311 3.334 3.356 8 1.860 2.217 2.416 2.553 2.657 2.740 2.809 2.868 2.919 2.965 3.006 3.043 3.076 3.107 3.136 3.163 3.187 3.211 3.233 3.253 9 1.833 2.180 2.372 2.504 2.604 2.683 2.750 2.807 2.856 2.900 2.939 2.974 3.007 3.036 3.064 3.090 3.113 3.136 3.157 3.177 10 1.812 2.151 2.338 2.466 2.562 2.640 2.704 2.759 2.807 2.849 2.887 2.921 2.953 2.982 3.008 3.033 3.056 3.078 3.098 3.117 11 1.796 2.127 2.310 2.435 2.529 2.605 2.667 2.721 2.768 2.809 2.846 2.879 2.910 2.938 2.963 2.988 3.010 3.031 3.051 3.070 12 1.782 2.108 2.287 2.410 2.502 2.576 2.638 2.690 2.735 2.776 2.812 2.845 2.874 2.902 2.927 2.951 2.972 2.993 3.012 3.031 13 1.771 2.092 2.269 2.389 2.480 2.552 2.613 2.664 2.709 2.748 2.784 2.816 2.845 2.872 2.897 2.920 2.941 2.961 2.980 2.998 14 1.761 2.079 2.253 2.371 2.461 2.532 2.592 2.642 2.686 2.725 2.760 2.791 2.820 2.847 2.871 2.894 2.915 2.935 2.953 2.971 15 1.753 2.067 2.239 2.356 2.444 2.515 2.573 2.623 2.667 2.705 2.740 2.771 2.799 2.825 2.849 2.871 2.892 2.912 2.930 2.948 16 1.746 2.057 2.227 2.343 2.430 2.500 2.558 2.607 2.650 2.688 2.722 2.753 2.781 2.806 2.830 2.852 2.873 2.892 2.910 2.927 17 1.740 2.048 2.217 2.332 2.418 2.487 2.544 2.593 2.635 2.673 2.706 2.737 2.764 2.790 2.813 2.835 2.856 2.875 2.893 2.909 18 1.734 2.040 2.208 2.321 2.407 2.475 2.532 2.580 2.622 2.660 2.693 2.723 2.750 2.775 2.799 2.820 2.840 2.859 2.877 2.894 19 1.729 2.033 2.200 2.312 2.397 2.465 2.521 2.569 2.611 2.648 2.681 2.711 2.738 2.763 2.786 2.807 2.827 2.846 2.863 2.880 20 1.725 2.027 2.192 2.304 2.389 2.456 2.512 2.559 2.601 2.637 2.670 2.699 2.726 2.751 2.774 2.795 2.815 2.834 2.851 2.867 120 1.658 1.934 2.083 2.183 2.259 2.318 2.368 2.410 2.446 2.478 2.507 2.533 2.557 2.579 2.599 2.617 2.634 2.651 2.666 2.680 32000 1.645 1.916 2.062 2.160 2.234 2.292 2.341 2.382 2.417 2.449 2.477 2.502 2.525 2.546 2.565 2.584 2.600 2.616 2.631 2.645 -1 1.645 1.916 2.062 2.160 2.234 2.292 2.340 2.381 2.417 2.448 2.476 2.502 2.525 2.546 2.565 2.583 2.600 2.616 2.631 2.645

Dunnett's test, one sided, alpha = 0.1 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 1.886 3 1.638 2.130 4 1.533 1.963 2.204 5 1.476 1.873 2.094 2.245 2.359 2.451 2.527 2.592 2.649 2.699 2.744 2.784 2.821 2.855 2.887 2.916 2.943 2.969 2.993 3.015 6 1.440 1.817 2.025 2.167 2.274 2.360 2.431 2.492 2.545 2.592 2.633 2.671 2.706 2.737 2.767 2.794 2.819 2.843 2.865 2.886 7 1.415 1.779 1.978 2.114 2.217 2.298 2.366 2.424 2.474 2.519 2.559 2.595 2.627 2.657 2.685 2.711 2.735 2.758 2.779 2.799 8 1.397 1.751 1.944 2.076 2.175 2.254 2.319 2.375 2.424 2.466 2.505 2.539 2.571 2.600 2.627 2.651 2.675 2.696 2.717 2.736 9 1.383 1.730 1.919 2.047 2.143 2.220 2.284 2.338 2.385 2.427 2.464 2.497 2.528 2.556 2.582 2.606 2.629 2.650 2.670 2.688 10 1.372 1.713 1.899 2.024 2.119 2.194 2.256 2.309 2.355 2.396 2.432 2.465 2.495 2.522 2.548 2.571 2.593 2.614 2.633 2.651 11 1.363 1.700 1.882 2.006 2.099 2.172 2.234 2.286 2.331 2.371 2.406 2.439 2.468 2.495 2.520 2.543 2.564 2.584 2.603 2.621 12 1.356 1.689 1.869 1.991 2.082 2.155 2.215 2.266 2.311 2.350 2.385 2.417 2.446 2.472 2.497 2.519 2.541 2.560 2.579 2.597 13 1.350 1.680 1.858 1.978 2.069 2.140 2.200 2.250 2.294 2.333 2.368 2.399 2.427 2.454 2.478 2.500 2.521 2.540 2.559 2.576 14 1.345 1.672 1.849 1.968 2.057 2.128 2.187 2.237 2.280 2.319 2.353 2.384 2.412 2.438 2.461 2.484 2.504 2.523 2.542 2.559 15 1.341 1.665 1.840 1.959 2.047 2.118 2.176 2.225 2.268 2.306 2.340 2.371 2.398 2.424 2.447 2.469 2.490 2.509 2.527 2.544 16 1.337 1.660 1.833 1.951 2.039 2.108 2.166 2.215 2.258 2.295 2.329 2.359 2.387 2.412 2.435 2.457 2.477 2.496 2.514 2.531 17 1.333 1.655 1.827 1.944 2.031 2.100 2.158 2.206 2.249 2.286 2.319 2.349 2.377 2.402 2.425 2.446 2.466 2.485 2.503 2.519 18 1.330 1.650 1.822 1.938 2.024 2.093 2.150 2.198 2.240 2.277 2.310 2.340 2.368 2.392 2.415 2.437 2.457 2.475 2.493 2.509 19 1.328 1.646 1.817 1.932 2.018 2.087 2.143 2.191 2.233 2.270 2.303 2.332 2.359 2.384 2.407 2.428 2.448 2.467 2.484 2.500 20 1.325 1.642 1.813 1.927 2.013 2.081 2.137 2.185 2.227 2.263 2.296 2.325 2.352 2.377 2.400 2.421 2.440 2.459 2.476 2.492 120 1.289 1.588 1.746 1.853 1.932 1.995 2.046 2.090 2.128 2.162 2.191 2.218 2.243 2.265 2.286 2.305 2.323 2.340 2.356 2.370 32000 1.282 1.577 1.734 1.838 1.916 1.978 2.029 2.072 2.109 2.142 2.172 2.198 2.222 2.244 2.264 2.283 2.301 2.317 2.333 2.347 -1 1.282 1.577 1.734 1.838 1.916 1.978 2.029 2.072 2.109 2.142 2.171 2.198 2.222 2.244 2.264 2.283 2.301 2.317 2.332 2.347

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Studentisierten Maximum test, one sided, alpha = 0.01 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 6.965 3 4.541 5.710 4 3.747 4.544 5.044 5 3.365 3.997 4.387 4.671 4.896 5.081 5.239 5.376 5.497 5.606 5.705 5.795 5.877 5.954 6.025 6.092 6.154 6.213 6.269 6.321 6 3.143 3.684 4.014 4.252 4.440 4.595 4.726 4.841 4.942 5.033 5.115 5.190 5.259 5.323 5.383 5.439 5.491 5.540 5.587 5.631 7 2.998 3.483 3.774 3.984 4.149 4.285 4.400 4.500 4.589 4.668 4.740 4.806 4.866 4.922 4.975 5.023 5.069 5.112 5.153 5.192 8 2.896 3.342 3.608 3.799 3.948 4.071 4.175 4.265 4.345 4.417 4.482 4.541 4.595 4.646 4.693 4.737 4.778 4.817 4.854 4.889 9 2.821 3.239 3.487 3.664 3.801 3.915 4.011 4.094 4.167 4.233 4.293 4.348 4.398 4.444 4.487 4.528 4.566 4.602 4.636 4.668 10 2.764 3.161 3.394 3.560 3.690 3.796 3.886 3.963 4.032 4.094 4.150 4.201 4.247 4.291 4.331 4.369 4.404 4.438 4.470 4.500 11 2.718 3.098 3.321 3.479 3.602 3.702 3.787 3.861 3.926 3.984 4.037 4.085 4.129 4.170 4.209 4.244 4.278 4.309 4.339 4.367 12 2.681 3.048 3.262 3.413 3.531 3.627 3.708 3.779 3.841 3.896 3.946 3.992 4.034 4.073 4.110 4.144 4.176 4.206 4.234 4.261 13 2.650 3.007 3.213 3.359 3.473 3.565 3.643 3.711 3.770 3.824 3.872 3.916 3.956 3.994 4.028 4.061 4.092 4.120 4.148 4.173 14 2.625 2.972 3.172 3.314 3.424 3.513 3.589 3.654 3.712 3.763 3.809 3.852 3.891 3.927 3.961 3.992 4.021 4.049 4.075 4.100 15 2.603 2.942 3.138 3.276 3.382 3.469 3.542 3.606 3.662 3.712 3.757 3.798 3.835 3.870 3.903 3.933 3.962 3.989 4.014 4.038 16 2.584 2.916 3.108 3.243 3.347 3.431 3.503 3.564 3.619 3.667 3.711 3.751 3.788 3.822 3.853 3.883 3.911 3.937 3.961 3.985 17 2.567 2.894 3.082 3.214 3.316 3.399 3.468 3.529 3.582 3.629 3.672 3.711 3.746 3.780 3.810 3.839 3.866 3.892 3.916 3.938 18 2.552 2.875 3.059 3.189 3.289 3.370 3.438 3.497 3.549 3.595 3.637 3.675 3.710 3.743 3.773 3.801 3.827 3.852 3.876 3.898 19 2.540 2.857 3.039 3.167 3.265 3.344 3.411 3.469 3.520 3.566 3.607 3.644 3.678 3.710 3.739 3.767 3.793 3.817 3.840 3.862 20 2.528 2.842 3.021 3.147 3.243 3.322 3.388 3.444 3.494 3.539 3.579 3.616 3.650 3.681 3.710 3.737 3.762 3.786 3.809 3.830 120 2.358 2.617 2.760 2.858 2.933 2.993 3.044 3.087 3.124 3.158 3.188 3.215 3.240 3.263 3.284 3.304 3.322 3.339 3.356 3.371 32000 2.327 2.575 2.712 2.806 2.877 2.934 2.982 3.022 3.058 3.089 3.117 3.143 3.166 3.188 3.208 3.226 3.243 3.260 3.275 3.290 -1 2.326 2.575 2.712 2.806 2.877 2.934 2.981 3.022 3.058 3.089 3.117 3.143 3.166 3.187 3.207 3.226 3.243 3.259 3.275 3.289


ROELEE 3.1 74


ROELEE 3.1 75

Dunnett's test, two sided, alpha = 0.01 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 9.925 3 5.841 6.974 4 4.604 5.364 5.809 5 4.032 4.628 4.975 5.219 5.406 5.557 5.683 5.792 5.887 5.971 6.047 6.116 6.178 6.236 6.290 6.339 6.386 6.429 6.471 6.509 6 3.707 4.212 4.506 4.712 4.869 4.997 5.104 5.196 5.276 5.347 5.411 5.470 5.523 5.572 5.617 5.659 5.699 5.736 5.771 5.803 7 3.499 3.948 4.208 4.389 4.529 4.642 4.736 4.817 4.888 4.951 5.008 5.059 5.106 5.150 5.190 5.227 5.262 5.295 5.326 5.355 8 3.355 3.766 4.002 4.168 4.295 4.397 4.483 4.557 4.621 4.679 4.730 4.777 4.820 4.859 4.896 4.930 4.961 4.991 5.019 5.046 9 3.250 3.633 3.853 4.006 4.124 4.219 4.299 4.367 4.427 4.480 4.528 4.571 4.611 4.648 4.681 4.713 4.742 4.770 4.796 4.821 10 3.169 3.531 3.739 3.883 3.994 4.084 4.159 4.223 4.279 4.329 4.374 4.415 4.452 4.487 4.519 4.548 4.576 4.602 4.627 4.650 11 3.106 3.452 3.649 3.787 3.893 3.978 4.049 4.110 4.164 4.211 4.254 4.293 4.328 4.361 4.391 4.419 4.446 4.470 4.494 4.516 12 3.055 3.387 3.577 3.709 3.811 3.892 3.960 4.019 4.070 4.116 4.157 4.194 4.228 4.259 4.288 4.315 4.340 4.364 4.387 4.408 13 3.012 3.335 3.518 3.646 3.743 3.822 3.888 3.944 3.994 4.038 4.077 4.113 4.146 4.176 4.204 4.230 4.254 4.277 4.299 4.319 14 2.977 3.290 3.468 3.592 3.687 3.763 3.827 3.882 3.930 3.972 4.011 4.045 4.077 4.106 4.133 4.158 4.182 4.204 4.225 4.245 15 2.947 3.253 3.426 3.547 3.639 3.713 3.776 3.829 3.875 3.917 3.954 3.988 4.019 4.047 4.073 4.098 4.121 4.142 4.163 4.182 16 2.921 3.220 3.390 3.508 3.598 3.671 3.731 3.783 3.829 3.869 3.905 3.938 3.968 3.996 4.022 4.046 4.068 4.089 4.109 4.128 17 2.898 3.192 3.359 3.474 3.563 3.634 3.693 3.744 3.788 3.828 3.863 3.896 3.925 3.952 3.977 4.001 4.023 4.043 4.062 4.081 18 2.878 3.168 3.331 3.445 3.531 3.601 3.659 3.709 3.753 3.792 3.826 3.858 3.887 3.914 3.938 3.961 3.983 4.003 4.022 4.040 19 2.861 3.146 3.307 3.419 3.504 3.572 3.630 3.679 3.722 3.760 3.794 3.825 3.853 3.879 3.904 3.926 3.947 3.967 3.986 4.003 20 2.845 3.127 3.285 3.395 3.479 3.547 3.603 3.651 3.694 3.731 3.765 3.795 3.823 3.849 3.873 3.895 3.916 3.935 3.954 3.971 120 2.618 2.846 2.972 3.059 3.125 3.177 3.221 3.259 3.292 3.321 3.347 3.370 3.392 3.412 3.430 3.447 3.463 3.478 3.492 3.505 32000 2.576 2.794 2.915 2.998 3.061 3.111 3.152 3.188 3.219 3.247 3.271 3.294 3.314 3.333 3.350 3.366 3.381 3.396 3.409 3.421 -1 2.576 2.794 2.915 2.998 3.060 3.110 3.152 3.188 3.219 3.246 3.271 3.294 3.314 3.333 3.350 3.366 3.381 3.395 3.409 3.421

Dunnett's test, two sided, alpha = 0.05 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 4.303 3 3.182 3.867 4 2.776 3.310 3.618 5 2.571 3.030 3.293 3.476 3.615 3.727 3.821 3.900 3.970 4.032 4.087 4.137 4.183 4.225 4.264 4.300 4.334 4.366 4.395 4.424 6 2.447 2.863 3.099 3.263 3.388 3.489 3.573 3.644 3.707 3.763 3.812 3.857 3.898 3.936 3.971 4.004 4.034 4.063 4.089 4.115 7 2.365 2.752 2.971 3.123 3.238 3.331 3.408 3.475 3.533 3.584 3.630 3.671 3.709 3.744 3.777 3.807 3.835 3.861 3.886 3.909 8 2.306 2.673 2.880 3.023 3.131 3.219 3.292 3.354 3.408 3.457 3.500 3.539 3.575 3.608 3.638 3.666 3.693 3.718 3.741 3.763 9 2.262 2.614 2.812 2.948 3.052 3.135 3.205 3.264 3.316 3.362 3.403 3.440 3.474 3.506 3.535 3.562 3.587 3.610 3.633 3.654 10 2.228 2.568 2.759 2.890 2.990 3.070 3.137 3.194 3.244 3.288 3.328 3.364 3.396 3.427 3.454 3.480 3.504 3.527 3.548 3.569 11 2.201 2.532 2.717 2.845 2.941 3.019 3.084 3.139 3.187 3.230 3.268 3.303 3.334 3.363 3.390 3.415 3.439 3.461 3.481 3.501 12 2.179 2.502 2.683 2.807 2.901 2.977 3.040 3.094 3.140 3.182 3.219 3.253 3.284 3.312 3.338 3.363 3.385 3.407 3.427 3.446 13 2.160 2.478 2.654 2.776 2.868 2.942 3.003 3.056 3.102 3.142 3.179 3.212 3.242 3.269 3.295 3.319 3.341 3.362 3.381 3.400 14 2.145 2.457 2.631 2.750 2.840 2.912 2.973 3.024 3.069 3.109 3.144 3.177 3.206 3.233 3.258 3.282 3.303 3.324 3.343 3.361 15 2.131 2.439 2.610 2.727 2.816 2.887 2.946 2.997 3.041 3.080 3.115 3.147 3.176 3.202 3.227 3.250 3.271 3.291 3.310 3.328 16 2.120 2.424 2.592 2.708 2.795 2.865 2.924 2.974 3.017 3.056 3.090 3.121 3.150 3.176 3.200 3.222 3.243 3.263 3.282 3.299 17 2.110 2.410 2.577 2.691 2.777 2.846 2.904 2.953 2.996 3.034 3.068 3.099 3.127 3.152 3.176 3.199 3.219 3.239 3.257 3.274 18 2.101 2.399 2.563 2.676 2.761 2.830 2.887 2.935 2.977 3.015 3.048 3.079 3.107 3.132 3.156 3.177 3.198 3.217 3.235 3.252 19 2.093 2.388 2.551 2.663 2.747 2.815 2.871 2.919 2.961 2.998 3.031 3.061 3.089 3.114 3.137 3.159 3.179 3.198 3.216 3.233 20 2.086 2.379 2.540 2.651 2.735 2.802 2.857 2.905 2.946 2.983 3.016 3.045 3.073 3.098 3.121 3.142 3.162 3.181 3.198 3.215 120 1.980 2.238 2.379 2.475 2.547 2.604 2.651 2.692 2.727 2.758 2.786 2.811 2.834 2.855 2.875 2.893 2.910 2.925 2.940 2.954 32000 1.960 2.212 2.349 2.442 2.512 2.567 2.613 2.652 2.686 2.716 2.743 2.768 2.790 2.810 2.829 2.846 2.863 2.878 2.892 2.906 -1 1.960 2.212 2.349 2.442 2.511 2.567 2.613 2.652 2.686 2.716 2.743 2.767 2.790 2.810 2.829 2.846 2.862 2.878 2.892 2.905

ROELEE 3.1 76

Steel test, one sided, alpha = 0.01 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 4 2.326 2.562 2.692 5 2.326 2.561 2.690 2.779 2.845 2.899 2.943 2.981 3.014 6 2.326 2.561 2.690 2.778 2.844 2.897 2.942 2.979 3.012 7 2.326 2.560 2.689 2.777 2.843 2.896 2.941 2.978 3.011 8 2.326 2.560 2.689 2.776 2.843 2.896 2.940 2.977 3.010 9 2.326 2.560 2.688 2.776 2.842 2.895 2.939 2.977 3.009 10 2.326 2.560 2.688 2.776 2.842 2.894 2.938 2.976 3.009 11 2.326 2.560 2.688 2.775 2.841 2.894 2.938 2.975 3.008 12 2.326 2.559 2.687 2.775 2.841 2.894 2.938 2.975 3.008 13 2.326 2.559 2.687 2.775 2.841 2.893 2.937 2.975 3.007 14 2.326 2.559 2.687 2.774 2.840 2.893 2.937 2.974 3.007 15 2.326 2.559 2.687 2.774 2.840 2.893 2.937 2.974 3.007 16 2.326 2.559 2.687 2.774 2.840 2.893 2.936 2.974 3.006 17 2.326 2.559 2.687 2.774 2.840 2.892 2.936 2.974 3.006 18 2.326 2.559 2.687 2.774 2.840 2.892 2.936 2.973 3.006 19 2.326 2.559 2.687 2.774 2.840 2.892 2.936 2.973 3.006 20 2.326 2.559 2.686 2.774 2.839 2.892 2.936 2.973 3.005


ROELEE 3.1 77

Steel test, two sided, alpha = 0.01 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 4 2.576 2.798 2.920 5 2.576 2.797 2.919 3.003 3.067 3.118 3.161 3.197 3.229 6 2.576 2.797 2.919 3.003 3.066 3.117 3.159 3.196 3.227 7 2.576 2.796 2.918 3.002 3.065 3.116 3.159 3.195 3.226 8 2.576 2.796 2.918 3.002 3.065 3.116 3.158 3.194 3.225 9 2.576 2.796 2.918 3.001 3.064 3.115 3.157 3.193 3.225 10 2.576 2.796 2.917 3.001 3.064 3.115 3.157 3.193 3.224 11 2.576 2.796 2.917 3.001 3.064 3.114 3.156 3.192 3.224 12 2.576 2.796 2.917 3.000 3.063 3.114 3.156 3.192 3.223 13 2.576 2.795 2.917 3.000 3.063 3.114 3.156 3.192 3.223 14 2.576 2.795 2.917 3.000 3.063 3.114 3.156 3.192 3.223 15 2.576 2.795 2.917 3.000 3.063 3.113 3.155 3.191 3.223 16 2.576 2.795 2.917 3.000 3.063 3.113 3.155 3.191 3.222 17 2.576 2.795 2.917 3.000 3.063 3.113 3.155 3.191 3.222 18 2.576 2.795 2.916 3.000 3.063 3.113 3.155 3.191 3.222 19 2.576 2.795 2.916 2.999 3.062 3.113 3.155 3.191 3.222 20 2.576 2.795 2.916 2.999 3.062 3.113 3.155 3.190 3.222


ROELEE 3.1 78

Steel test, one sided, alpha = 0.01, Critical values for Sum of Ranks of Control Group, Equal numbers in all control and comparison groups Number of Comparison Groups 1 2 3 4 5 6 7 8 9 4 9.941 9.125 8.676 5 16.363 15.239 14.620 14.198 13.879 13.623 13.411 13.230 13.072 6 24.472 23.008 22.203 21.653 21.238 20.906 20.629 20.394 20.188 7 34.293 32.461 31.455 30.767 30.247 29.832 29.487 29.192 28.935 8 45.848 43.623 42.399 41.564 40.933 40.428 40.009 39.651 39.339 9 59.154 56.510 55.056 54.064 53.314 52.715 52.217 51.792 51.421 10 74.225 71.138 69.442 68.283 67.409 66.710 66.129 65.632 65.200 11 91.072 87.521 85.570 84.237 83.232 82.427 81.759 81.188 80.691 12 109.706 105.669 103.452 101.937 100.794 99.880 99.120 98.472 97.907 13 130.136 125.593 123.098 121.394 120.108 119.079 118.225 117.495 116.860 14 152.369 147.301 144.518 142.617 141.182 140.035 139.082 138.268 137.559 15 176.413 170.801 167.719 165.614 164.026 162.756 161.700 160.799 160.015 16 202.274 196.100 192.710 190.394 188.647 187.249 186.088 185.097 184.234 17 229.958 223.204 219.495 216.963 215.051 213.523 212.253 211.169 210.225 18 259.470 252.119 248.083 245.327 243.247 241.583 240.202 239.022 237.995 19 290.815 282.851 278.478 275.491 273.238 271.436 269.939 268.661 267.548 20 323.997 315.404 310.685 307.463 305.031 303.087 301.472 300.092 298.892


ROELEE 3.1 79



ROELEE 3.1 80

Appendix 1B

Ahner-Passing Module subroutine mvtvfe(d_erg, d_aw, w_df, w_ip, d_c, d_hvek, 1 d_cr4, P2Tail ) c adapted from AHNER/PASSING, Multivariate t test and simultaneous c comparisons versus a control group, c EDV in Medizin und Biologie 14 (3-4), 113-120, ISSN 0300-8282 C This subroutine calculates the Prob of T <= d_aw, where c T is the test statistics, d_aw will usually be the realised value c of the test statistic. implicit integer*2 (a-z) parameter(noGPts=24) ! number of integration points ccc ! used as + and - to give 48 points in all real *8 d_erg, d_aw, d_c(*), d_hvek(*), d_cr4(*) 1 , d_GaussWt(noGPts), d_GaussAbs(noGPts) 1 , d_sum, d_Gwt, d_x 1 , d_suman 1 , d_an, d_bn, d_eq2 1 , d_h 1 , d_rootdf, d_root2f, d_ci 1 , d_small integer *2 w_df, w_ip, P2Tail, w_i, w_it 1 , sortI2(200) parameter(d_small=0.1d-20) c The Aproximate Integration the multivariant T-distribution c differential correlations matrix. c c Calls these routines c Quag2e() c Quag3e() c sort_double() c d_cr4 := array used for sorting c w_ip := number of values in cr4 c c INPUT c c d_aw: usually value of the test statistic c c w_df: degrees of freedom denominator c set as -9 for infinite degrees of freedom c c w_ip: degrees of freedom numerator c - number of simultaneous hypotheses being tested c c d_c: vector containing coefficient c out of the correlations matrix c c OUTPUT: c c d_erg: value from integrals c c work vectors: c c d_hvek c c d_cr4 c c DATA: c d_GaussAbs : abscissa for Gaussian integration with 48 points c d_GaussWt : weights for Gaussian integration with 48 points c see Abramowitz and Stegun, Page 917, Table 25.4 DATA d_GaussAbs/ 1 0.032380170962869 1 ,0.097004699209463

ROELEE 3.1 81

1 ,0.161222356068892 1 ,0.224763790394689 1 ,0.287362487355456 1 ,0.348755886292161 1 ,0.408686481990717 1 ,0.466902904750958 1 ,0.523160974722233 1 ,0.577224726083973 1 ,0.628867396776514 1 ,0.677872379632664 1 ,0.724034130923815 1 ,0.767159032515740 1 ,0.807066204029443 1 ,0.843588261624394 1 ,0.876572020274248 1 ,0.905879136715570 1 ,0.931386690706554 1 ,0.952987703160431 1 ,0.970591592546247 1 ,0.984124583722827 1 ,0.993530172266351 1 ,0.998771007252426/ c 1 0.095012509837637, 0.281603550779259, 0.458016777657227, c 2 0.617876244402644, 0.755404408355003, 0.865631202387832, c 3 0.944575023073233, 0.989400934991650/ DATA d_GaussWt/ 1 0.064737696812684 1 ,0.064466164435950 1 ,0.063924238584648 1 ,0.063114192286254 1 ,0.062039423159893 1 ,0.060704439165894 1 ,0.059114839698396 1 ,0.057277292100403 1 ,0.055199503699984 1 ,0.052890189485194 1 ,0.050359035553854 1 ,0.047616658492490 1 ,0.044674560856694 1 ,0.041545082943465 1 ,0.038241351065831 1 ,0.034777222564770 1 ,0.031167227832798 1 ,0.027426509708357 1 ,0.023570760839324 1 ,0.019616160457356 1 ,0.015579315722944 1 ,0.011477234579235 1 ,0.007327553901276 1 ,0.003153346052306/ c 1 0.189450610455068, 0.182603415044924, 0.169156519395003, c 2 0.149595988816577, 0.124628971255534, 0.095158511682493, c 3 0.062253523938648, 0.027152459411754/ c c The Aproximate Integration the multivariant T-distribution c determined from d_an and d_bn c formula (17) and (19) if(w_df.gt.0) then d_rootdf = DSQRT( DFLOAT(w_df) ) d_root2f=DSQRT(2.0D0) * d_rootdf d_an= (w_df-5.0D0*d_root2f)/2.0D0 if(d_an .LE. 0.0) then d_an=0.0D0 else d_an=DSQRT(d_an) endif d_bn=DSQRT( (w_df+5.0*d_root2f)/2.0D0 ) if(w_df .LT. 100) then if(d_bn .LT. 10.0) d_bn = 10.0D0 endif endif

ROELEE 3.1 82

c sort the d_c(i) do w_i=1,w_ip d_cr4(w_i) = d_c(w_i) enddo call sort_double(d_c, sortI2, w_ip) do w_i=1, w_ip d_c(w_i) = d_cr4(sortI2(w_i)) enddo c calculation constant work value = 1/SQ ROOT (1-ci**2) do w_i=1, w_ip d_ci = d_c(w_i) d_hvek(w_i) = 1.0D0/ DSQRT( 1.0D0 - d_ci*d_ci) enddo c c outer integration c Gauss integration with 48 weight points c formula(14) d_sum = 0.0D0 do w_it=1, noGPts d_Gwt = d_GaussWt(w_it) d_x = d_GaussAbs(w_it) call quag2e(d_eq2, d_x, d_aw, w_df, w_ip, d_an, d_bn, 1 d_c, d_h, 1 d_rootdf, d_hvek, P2Tail) if(DABS(d_eq2).gt.d_small) then d_suman = d_Gwt * d_eq2 d_sum = d_sum+d_suman endif d_x = -d_x call quag2e(d_eq2, d_x, d_aw, w_df, w_ip, d_an, d_bn, 1 d_c, d_h, 1 d_rootdf, d_hvek, P2Tail) if(DABS(d_eq2).gt.d_small) then d_suman = d_Gwt * d_eq2 d_sum = d_sum + d_suman endif enddo 990 continue if(P2Tail.eq.-1) then d_erg= 1.0D0 - d_sum else d_erg= d_sum endif return end subroutine quag2e(d_eq2, d_x, d_aw, w_df, w_ip, d_an, d_bn, 1 d_c, d_h, 1 d_rootdf, d_hvek, P2Tail) c Calculation value from integrand on the nullstelle c formula (14) implicit integer*2 (a-z) parameter(noGPts=24) ! number of integration points ccc ! used as + and - to give 48 points in all real*8 d_eq2, d_x, d_aw, d_an, d_bn 1 , d_c(*), d_h, d_rootdf, d_hvek(*) 1 , d_Gwt, d_y 1 , d_GaussAbs(noGPts), d_GaussWt(noGPts) 1 , d_w 1 , d_f13a 1 , d_f15, d_f15w, d_logf15w 1 , d_f19a, d_f19b, d_f19c 1 , d_f20, d_f20a, d_f20b, d_f20c, d_f20w 1 , d_sum, d_suman 1 , quag3e, quagl3 1 , PI, RTPI, RT2PI, G15

ROELEE 3.1 83

1 , d_small, d_q integer *2 w_df, w_ip, P2Tail 1 , w_df1, w_df2, w_j, w_it parameter(PI = 3.141592653589793D0) parameter(RT2PI = 2.506628274631001D0) parameter(RTPI = 1.772453850905516D0) parameter(G15 = 0.8862269255D0) ! Gamma (1.5) parameter(d_small = 0.1d-20) c d_GaussAbs : abscissa for Gaussian integration with 48 points c d_GaussWt : weights for Gaussian integration with 48 points c see Abramowitz and Stegun, Page 917, Table 25.4 DATA d_GaussAbs/ 1 0.032380170962869 1 ,0.097004699209463 1 ,0.161222356068892 1 ,0.224763790394689 1 ,0.287362487355456 1 ,0.348755886292161 1 ,0.408686481990717 1 ,0.466902904750958 1 ,0.523160974722233 1 ,0.577224726083973 1 ,0.628867396776514 1 ,0.677872379632664 1 ,0.724034130923815 1 ,0.767159032515740 1 ,0.807066204029443 1 ,0.843588261624394 1 ,0.876572020274248 1 ,0.905879136715570 1 ,0.931386690706554 1 ,0.952987703160431 1 ,0.970591592546247 1 ,0.984124583722827 1 ,0.993530172266351 1 ,0.998771007252426/ c 1 0.095012509837637, 0.281603550779259, 0.458016777657227, c 2 0.617876244402644, 0.755404408355003, 0.865631202387832, c 3 0.944575023073233, 0.989400934991650/ DATA d_GaussWt/ 1 0.064737696812684 1 ,0.064466164435950 1 ,0.063924238584648 1 ,0.063114192286254 1 ,0.062039423159893 1 ,0.060704439165894 1 ,0.059114839698396 1 ,0.057277292100403 1 ,0.055199503699984 1 ,0.052890189485194 1 ,0.050359035553854 1 ,0.047616658492490 1 ,0.044674560856694 1 ,0.041545082943465 1 ,0.038241351065831 1 ,0.034777222564770 1 ,0.031167227832798 1 ,0.027426509708357 1 ,0.023570760839324 1 ,0.019616160457356 1 ,0.015579315722944 1 ,0.011477234579235 1 ,0.007327553901276 1 ,0.003153346052306/ c 1 0.189450610455068, 0.182603415044924, 0.169156519395003, c 2 0.149595988816577, 0.124628971255534, 0.095158511682493, c 3 0.062253523938648, 0.027152459411754/ c formula (20)

ROELEE 3.1 84

d_f20(d_w) = (d_f20a - d_f20b)*0.5D0*(d_w+1.0D0)+d_f20b c [ ] in formula (19) d_f19a(d_w)= d_f20w * d_f20w - 1.0D0 1 - DLOG( DFLOAT(w_df) / DFLOAT(w_df - 2) ) c remainder from outer 10 in formula (19) d_f19b(d_w)= -1.0D0 + (w_df -1.0D0) * DLOG(d_f20w) c outer 10 in formula (19) d_f19c(d_w) = DEXP(- (w_df*0.5D0) *d_f19a(d_w) + d_f19b(d_w) ) c formula (15) d_f15(d_w) = (d_bn - d_an) * 0.5D0 * (d_w + 1.0D0) +d_an c part of formula (13) d_f13a(d_w) =DEXP(- (d_f15w * d_f15w) ) w_df2 = w_df/2 if(w_df .LT. 0 ) then ! df = infinity d_h = 5.0D0 / (2.0D0* PI ) d_h = d_h * DEXP(-12.5D0*d_x*d_x) else if(w_df .GE. 100 ) then c Calculation d_h for df >= 100 c Formula (19) d_f20c = 5.0D0*DSQRT(2.0D0)/d_rootdf d_f20a = DSQRT( 1.0D0 + d_f20c) d_f20b = DSQRT( 1.0D0 - d_f20c) d_f20w = d_f20(d_x) d_h = (d_bn - d_an) 1 * DSQRT( DFLOAT( w_df-2) / DFLOAT(w_df) ) 1 * d_f19c(d_x) d_h = d_h / (2.0D0* PI ) d_h = d_h /(1.0D0 + 1.0D0/(6.0D0*DFLOAT(w_df -2) )) else c Calculation d_h for w_df < 100 c Formula (16) ccc ! calculate formula in LOG form to stop underflow w_df1 = w_df -1 d_f15w = d_f15(d_x) ! xi from Formula (15) d_h = DLOG(d_bn - d_an) ! 2 cancels with 2 in Formula (13) d_h = d_h- DLOG( RT2PI) d_logf15w = DLOG(d_f15w) ccc ! divide by Gamma Function - see Formula (13) ccc ! multiply by xi**(f-1) do w_j=1, w_df1 d_h = d_h + d_logf15w ! (xi ** (f-1) term) if( w_j .LE. (w_df2 - 1) ) then if( MOD(w_df,2) .EQ. 0) then ccc note log(1) = zero if(w_j.gt.1) d_h = d_h - DLOG(DFLOAT(w_j)) else d_h = d_h - DLOG(DFLOAT(w_j) + 0.5D0) endif endif enddo if( MOD(w_df,2) .NE. 0) 1 d_h = d_h- DLOG(G15) ccc finally for Gamma divide by Gamma(1.5) when w_df is odd ccc d_h = d_h * d_f13a(d_x) ! mult by exp(-xi**2) - Formula (13) d_h = d_h - (d_f15w * d_f15w) if(d_h.gt.DLOG(d_small))

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1 d_h = DEXP(d_h) ! back from LOG form endif d_eq2 = 0.0D0 if(d_h.lt.d_small) go to 990 ! beware underflow c Inner integration c Gauss integration with 48 points c value from d_h * [ ] in formula (14) d_sum = 0.0 do w_it=1, noGPts d_Gwt = d_GaussWt(w_it) d_y = d_GaussAbs(w_it) if(P2Tail.eq.0) then d_suman = quagl3(d_y, d_x, d_aw, w_df, w_ip, 1 d_an, d_bn, d_c, d_rootdf, d_hvek) else d_suman = quag3e(d_y, d_x, d_aw, w_df, w_ip, 1 d_an, d_bn, d_c, d_rootdf, d_hvek) endif if(DABS(d_suman).gt.d_small) d_sum = d_sum + d_suman*d_Gwt d_y = -d_y if(P2Tail.eq.0) then d_suman = quagl3(d_y, d_x, d_aw, w_df, w_ip, 1 d_an, d_bn, d_c, d_rootdf, d_hvek) else d_suman = quag3e(d_y, d_x, d_aw, w_df, w_ip, 1 d_an, d_bn, d_c, d_rootdf, d_hvek) endif if(DABS(d_suman).gt.d_small) d_sum = d_sum + d_suman*d_Gwt enddo if(DABS(d_sum).gt.d_small) d_eq2 = d_sum * d_h 990 continue return end function quag3e(d_y, d_x, d_aw, w_df, w_ip, 1 d_an, d_bn, d_c, d_rootdf, d_hvek) c calculate value from inner integral c from [ ] in formula (14) c for one-sided tests real *8 quag3e 1 , d_y, d_x, d_aw, d_an, d_bn, d_c(*) 1 , d_rootdf, d_hvek(*), d_hveki 1 , d_f15, d_f15w 1 , d_d1 1 , d_w, d_u, d_v 1 , d_ci, d_r, d_y2 1 , d_g, d_ar 1 , ROOT2, RT12_5, Nprob integer *2 w_df, w_ip, w_i c formula (15) d_f15(d_w) = (d_bn-d_an) * 0.5D0 * (d_w+1.0D0) + d_an c formula (11) d_d1(d_u,d_v) = (d_aw * d_u /d_rootdf + d_ci*d_v) 1 * d_hveki ROOT2 = DSQRT(2.0D0) RT12_5 = DSQRT(12.5D0) c now calcuate outer [ ] in formula (14) d_g = 5.0D0 * DEXP( -12.5D0 * d_y * d_y)

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if(w_df.gt.0) d_f15w = d_f15(d_x) ! xi(z) d_y2 = RT12_5*d_y ! 5/ROOT(2) w do w_i=1, w_ip if( w_i .gt. 1 ) then if( DABS( d_c(w_i)-d_c(w_i-1) ) .LT. 1.0D-5 ) goto 80 endif d_ci = d_c(w_i) c standard normal distribution function in formula (14) d_hveki = d_hvek(w_i) if(w_df.lt.0) then ! infinite d. of f d_r = ( d_aw + ROOT2*d_ci*d_y2) * d_hveki else d_r = ROOT2*d_d1(d_f15w, d_y2) endif d_ar = Nprob(d_r) 80 continue d_g = d_g * d_ar enddo quag3e = d_g return end function quagl3(d_y, d_x, d_aw, w_df, w_ip, 1 d_an, d_bn, d_c, d_rootdf, d_hvek) c calculate value from inner integral c from [ ] in formula (14) on the nullstell ( null position ?? ) c for two sided tests real *8 quagl3 1 , d_y, d_x, d_aw, d_an, d_bn, d_c(*) 1 , d_rootdf, d_hvek(*), d_hveki 1 , d_f15, d_f15w 1 , d_d1, d_d3 1 , d_w, d_u, d_v 1 , d_ci, d_r, d_y2 1 , d_g, d_ar, d_s, d_as 1 , ROOT2, RT12_5, Nprob integer *2 w_df, w_ip, w_i c formula (15) d_f15(d_w) = (d_bn-d_an) * 0.5D0 * (d_w+1.0D0) + d_an c formula (21) 10 brackets part 1 d_d1(d_u,d_v) = (d_aw * d_u /d_rootdf + d_ci*d_v) 1 * d_hveki c formula (21) 10 brackets part 2 d_d3(d_u,d_v) = (-d_aw * d_u /d_rootdf + d_ci*d_v) 1 * d_hveki ROOT2 = DSQRT(2.0D0) RT12_5 = DSQRT(12.5D0) c now calculate outer [ ] in formula (14) d_g = 5.0D0 * DEXP( -12.5D0 * d_y * d_y) if(w_df.gt.0) d_f15w = d_f15(d_x) ! xi(z) d_y2 = RT12_5*d_y ! 5/ROOT(2) w do w_i=1, w_ip if( w_i .GT. 1 ) then if( DABS( d_c(w_i)-d_c(w_i-1) ) .LT. 1.0D-5 ) goto 80 endif d_ci = d_c(w_i) d_hveki = d_hvek(w_i)

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c standard normal distribution function in formula (21) if(w_df.lt.0) then ! infinite degrees of freedom d_hveki = d_hvek(w_i) d_r = ( d_aw + ROOT2*d_ci*d_y2) * d_hveki else d_r = ROOT2*d_d1(d_f15w,d_y2) endif d_ar = Nprob(d_r) c 2. standard normal distribution function in formula (21) if(w_df.lt.0) then ! infinite degrees of freedom d_s = ( -d_aw + ROOT2*d_ci*d_y2) * d_hveki else d_s = ROOT2*d_d3(d_f15w,d_y2) endif d_as = Nprob(d_s) 80 continue d_g = d_g * (d_ar - d_as) enddo quagl3 = d_g return end SUBROUTINE sort_double(vector, sortI2, N) c c routine to sort vector into ascending order c sortI2 holds sort order for vector c N is the number of items c implicit integer*2 (a-z) real*8 vector(*), BI, BN integer*2 sortI2(*) DO i=1, N BN = vector(i) pmax = i -1 pmin = 1 I1 = 0 3 continue if(pmin.le.pmax) then I1 = pmin + (pmax-pmin+1)/2 NI = sortI2(I1) BI = vector(NI) IF(BN.LT.BI) then I1 = I1 -1 pmax = I1 GO TO 3 else if(BN.GT.BI) then pmin = I1 if(pmax.gt.pmin) go to 3 ENDIF ENDIF do p= N-1,I1+1, -1 sortI2(p+1) = sortI2(p) enddo sortI2(I1+1) = i enddo 990 continue RETURN END function InvAhnPass(alph, df, w_nhyp, d_c, d_hvek, d_cr4, P2Tail) ccc ccc inverse Ahner Passing function, i.e. x such that ccc integral -inf to x = alph ccc JSF 24.7.90 ccc implicit integer*2 (a-z) real*8 InvAhnPass, alph, x1, x2, xnew, anew 1 , xmax, xmin, xsmall 1 , d_c(*), d_hvek(*), d_cr4(*)

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integer*2 df, w_nhyp, P2Tail parameter( xmax=10.0D0, xmin = -xmax, xsmall=1.0d-5) if(alph.le.(0.0)) then xnew = xmin go to 990 else if(alph.ge.(1.0)) then xnew = xmax go to 990 endif x1 = xmax x2 = xmin if(P2Tail.eq.0) then ! 2-sided prob x2=0.0D0 endif 10 continue xnew = (x1+x2)/2.0 call mvtvfe(anew, xnew, df, w_nhyp, d_c, d_hvek, d_cr4, P2Tail) if(anew.ge.alph) x1=xnew if(anew.le.alph) x2=xnew if(x1-x2.gt.xsmall) go to 10 990 continue InvAhnPass = xnew return end ______________________________________________________________________

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Appendix 2A

Bonferroni Results

name Orig P Bonferroni Holm Hommel Hochberg Example 1: Effects of exposure to lead T-1 0.370000 1.000000 1.000000 1.000000 1.000000 T-2 0.900000 1.000000 1.000000 1.000000 1.000000 T-3 0.420000 1.000000 1.000000 1.000000 1.000000 T-4 0.050000 1.000000 1.000000 1.000000 1.000000 RT-1 0.320000 1.000000 1.000000 1.000000 1.000000 RT-2 0.001000 0.050000 0.050000 0.050000 0.050000 RT-3 0.001000 0.050000 0.050000 0.050000 0.050000 RT-4 0.010000 1.000000 0.100000 0.100000 0.100000 R-A 0.002000 0.050000 0.050000 0.050000 0.050000 R-B 0.030000 1.000000 1.000000 1.000000 1.000000 R-C 0.070000 1.000000 1.000000 1.000000 1.000000 SR 0.040000 1.000000 1.000000 1.000000 1.000000 Example 2: Sleep patterns 1 0.560000 1.000000 1.000000 1.000000 1.000000 2 0.500000 1.000000 1.000000 1.000000 1.000000 3 0.440000 1.000000 1.000000 1.000000 1.000000 4 0.400000 1.000000 1.000000 1.000000 1.000000 5 0.340000 1.000000 1.000000 1.000000 1.000000 6 0.280000 1.000000 1.000000 1.000000 1.000000 7 0.260000 1.000000 1.000000 1.000000 1.000000 8 0.240000 1.000000 1.000000 1.000000 1.000000 9 0.180000 1.000000 1.000000 1.000000 1.000000 10 0.180000 1.000000 1.000000 1.000000 1.000000 11 0.160000 1.000000 1.000000 1.000000 1.000000 12 0.080000 1.000000 1.000000 1.000000 1.000000 13 0.040000 1.000000 1.000000 1.000000 1.000000 14 0.040000 1.000000 1.000000 1.000000 1.000000 15 0.020000 1.000000 1.000000 1.000000 1.000000 16 0.004000 0.100000 0.100000 0.100000 0.100000 17 0.001000 0.050000 0.050000 0.050000 0.050000 18 0.001000 0.050000 0.050000 0.050000 0.050000 19 0.001000 0.050000 0.050000 0.050000 0.050000 20 0.001000 0.050000 0.050000 0.050000 0.050000 21 0.001000 0.050000 0.050000 0.050000 0.050000 22 0.001000 0.050000 0.050000 0.050000 0.050000

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Appendix 2B

Bonferroni Module cccc ccc routine to perform Bonferroni adjustment to a set of probs ccc JSF 5.1.95 subroutine Bonfadj(P,PA,flev,w_bmode,w_rnProb,d_rlProb, 1 d_inputP,d_outputP) ccc ccc P - probs to be adjusted ccc PA - adjusted probs ccc flev - maximum possible levels ccc bmode - mode of adjustment to use (see below) ccc rnProb - number of alpha levels of interest ccc rlProb - values for the alpha levels ccc such as 0.1, 0.05, 0.01, 0.001 ccc d_inputP - work vector for probs to be adjusted ccc d_outputP - work vector for adjusted probs ccc implicit integer*2 (a-z) real*8 P(*), PA(*) 1 , d_rlprob(*) 1 , d_inputP(*), d_outputP(*) 1 , d_small integer*2 w_nP, w_bmode, w_rnProb 1 , w_i d_small = 0.1d-20 w_nP = 0 do w_i=1, flev if(P(w_i).ge. d_small) then w_nP = w_nP +1 d_inputP(w_nP) = P(w_i) endif enddo call bonferroni(d_inputP, d_outputP, w_nP, w_bmode, 1 w_rnProb, d_rlprob) w_nP = 0 do w_i=1, flev if(P(w_i).ge. d_small) then w_nP = w_nP +1 PA(w_i) = d_outputP(w_nP) else PA(w_i) = P(w_i) endif enddo return end subroutine bonferroni(d_inputP, d_outputP, w_nP, w_bmode, 1 w_rnProb, d_rlprob) cccc ccc routine to perform Bonferroni adjustment to a set of probs ccc JSF 30.11.94 ccc ccc inputP - original probs ccc outputP - adjusted probs - set probs as NS (value 1.0) or ccc just less than most extreme alpha level ccc nP - number of probs of interest (independent hypotheses) ccc bmode - mode of adjustment to use: ccc 1) simple adjustment - share over probs equally ccc 2) Bonferroni-Holm alpha adjustment ccc 3) Hochberg-Hommel alpha adjustment ccc 4) Hochberg alpha adjustment ccc ccc rnProb - number of alpha levels of interest ccc rlProb - values for the alpha levels ccc such as 0.1, 0.05, 0.01, 0.001 implicit integer*2 (a-z) real*8 d_inputP(*), d_outputP(*), d_rlprob(*) 1 , d_Pi, d_xsmall, d_alpha integer*2 w_nP, w_bmode, w_rnProb

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1 , w_i, w_j, w_k, w_alph, w_jmax, w_ip 1 , sortI2(200) 1 , w_nPstop 1 , w_accept(200) parameter(d_xsmall=0.1d-6) do w_i=1, w_nP d_outputP(w_i) = 1.0D0 w_accept (w_i) = 0 ! mark hypotheses as not accepted enddo if(w_bmode.eq.1) then ! simple Bonferroni adjustment ccc Pi are p-values corresponding to hypotheses Hi ccc then if there are m hypotheses ccc reject Hi when Pi <= alpha/m ccc do w_i=1, w_nP d_Pi = d_inputP(w_i)*DFLOAT(w_nP) do w_alph=1, w_rnProb d_alpha = d_rlprob(w_alph) if(d_Pi.gt.d_alpha) then if(w_alph.eq.1) then ! not significant at all d_Pi = 1.0D0 else ! set significant at previous alpha level d_Pi = d_rlprob(w_alph-1) - d_xsmall endif go to 10 endif enddo ccc ! P level significant at lowest ccc ! alpha level - use this P value 10 continue d_outputP(w_i) = d_Pi enddo else if(w_bmode.eq.2) then ccc ! Bonferroni-Holm alpha adjustment ccc ! see Hochberg, A Sharper Bonferroni procedure ccc for multiple tests of significance ccc Biometrika (1988) 75, 4, pp 800-802 ccc p(1),..., p(m) are the ordered p-values, ccc with H(1),... H(m) the corresponding hypotheses ccc Reject H(i) when for all j=1,...,i ccc p(j) <= alpha/(m-j+1) ccc call sort_double(d_inputP, sortI2, w_nP) ccc sortI2 holds the order to sort P values into ascending order w_nPstop = w_nP do w_alph=1, w_rnProb d_alpha = d_rlprob(w_alph) do w_i=1, w_nPstop w_ip = sortI2(w_i) d_Pi = d_inputP(w_ip)*DFLOAT(w_nP - w_i +1) if(d_Pi.gt.d_alpha) then if(w_alph.eq.1) then ! not significant at all d_Pi = 1.0D0 else ! set significant at previous alpha level d_Pi = d_rlprob(w_alph-1) - d_xsmall endif ccc ! all higher prob Hyps set sig level do w_j=w_i, w_nPstop w_ip = sortI2(w_j) d_outputP(w_ip) = d_Pi enddo w_nPstop = w_i -1 ! we now have wanted probs for all ccc ! levels >= this one, for all ALPHA's go to 20 endif ccc ! P level significant at lowest ccc ! alpha level d_outputP(w_ip) = d_alpha - d_xsmall enddo 20 continue enddo

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else if(w_bmode.eq.3) then ccc 3) Hochberg-Hommel alpha adjustment ccc ! see Hommel, A comparison of two modified ccc Bonferroni procedures ccc Biometrika (1989) 76, 3, pp 624-625 ccc p(1),..., p(m) are the ordered p-values, ccc with H(1),... H(m) the corresponding hypotheses ccc Let J = {i' such that p(m-i'+k) > k.alpha/i',k=1,..,i'} ccc Reject Hi when pi <= alpha/j', with j'=max J ccc if J empty, reject all Hi, i=1,..,m ccc call sort_double(d_inputP, sortI2, w_nP) ccc sortI2 holds the order to sort P values into ascending order do w_alph=1, w_rnProb d_alpha = d_rlProb(w_alph) ccc find j' = max J w_jmax = 0 do w_i=1, w_nP do w_k=1, w_i w_ip = sortI2(w_nP - w_i +w_k) d_Pi = DFLOAT(w_i)*d_inputP(w_ip)/DFLOAT(w_k) if(d_Pi .le. d_alpha) go to 30 enddo w_jmax = w_i enddo 30 continue do w_i=1, w_nP if(w_accept(w_i).eq.1) then ccc ! Hypothesis accepted at previous alpha level ccc ! do not change value else if(w_jmax.eq.0) then ccc ! J empty - reject all hyp at this level d_outputP(w_i) = d_alpha - d_xsmall else ! reject if Pi <= alpha/max J d_Pi = DFLOAT(w_jmax)*d_inputP(w_i) if(d_Pi.gt.d_alpha) then if(w_alph.eq.1) then ! not significant at all d_Pi = 1.0D0 else ! set significant at previous alpha level d_Pi = d_rlprob(w_alph-1) - d_xsmall endif w_accept(w_i) = 1 else d_Pi = d_alpha - d_xsmall endif d_outputP(w_i) = d_Pi endif enddo enddo else if(w_bmode.eq.4) then ccc ! Hochberg procedure ccc ! Hochberg and Benjamini, More powerful procedures ccc ! for multiple significance testing ccc ! Statistics in Medicine, Vol 9, 811-818 (1990) ccc Generally one proceeds from the highest to the lower p-values ccc retaining H(i) if its p-value satisfies p(i) > alpha/(m-i+1) ccc One stops the procedure at the first ordered hypothesis with ccc lower or equal p-values. ccc call sort_double(d_inputP, sortI2, w_nP) ccc sortI2 holds the order to sort P values into ascending order do w_alph=1, w_rnProb d_alpha = d_rlprob(w_alph) do w_i=1, w_nP w_ip = sortI2(w_nP -w_i +1) ! take values in reverse order d_Pi = d_inputP(w_ip)*DFLOAT(w_i) if(d_Pi.gt.d_alpha) then if(w_accept(w_ip).eq.0) then if(w_alph.eq.1) then ! not significant at all d_Pi = 1.0D0 else ! set significant at previous alpha level d_Pi = d_rlprob(w_alph-1) - d_xsmall endif

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d_outputP(w_ip) = d_Pi endif w_accept(w_ip) = 1 else ! stop procedure setting ccc ! all lower prob Hyps set sig level d_Pi = d_alpha - d_xsmall do w_j= w_i, w_nP w_ip = sortI2(w_nP -w_j +1) d_outputP(w_ip) = d_Pi enddo go to 40 endif enddo 40 continue enddo endif return end __________________________________________________________________

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Appendix 3A

Command File TSTATS1.CMD ++ *** + *** Command File TSTAT1.CMD + *** Used to test DATATOX F1 Statistics + *** Standard RoeLee Statistics - + *** 1. Fisher's Exact Test + *** 2. Kruskal-Wallis non-parametric analysis of Variance + *** 3. One way analysis of variance + *** 4. Chi-squared test + *** 5. Time adjusted chi-squared test for fatal conditions + *** 6. Peto analysis + *** 7. Exact trend test + *** 8. stratified Kruskal-Wallis test (Fry-Lee test) + *** 9. Peto visible analysis + ++ SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SELECT SET SEX 3 SET PARTITION 0 SET STRATA 0 .SET LAYOUT $35 Text layout options $35 $35 1) Paper width: 120 $35 2) Paper length: 64 $35 3) Window top margin: 5 $35 4) Window bottom margin: 4 $35 5) Window left margin: 5 $35 6) Window right margin: 5 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 2 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 10 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 15 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 33 $35 17) Number of columns between groups: 2 $35 SET FACTOR SEX SET FACTOR GROUP .SET HEADING $36 Headings on output $36 $36 1 :C:Appendix 3B - Table $36 2 :C: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C:[analysis description] $36 5 :C: $36 6 :L:[reserved for system] $36 7 :L: $36 8 :L:[reserved for system] $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation $36 $36 further heading for group comparison analyses $36 11:L: Group Group Group Group $36 12:L: 1 2 3 4 $36 13:L: Control Low Middle High $36 14TB: T T T T $36 .SET FOOT

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$53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 .SET PAGE $45 Page numbers $45 $45 1) First Page number: (0 for none) 1 $45 2) Page number: 1)Top or 2)Bottom 2 $45 3) Page number: 1)Right, 2)Centre or 3)Left 1 $45 $45 SET TAB 1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 $17 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 1 1 1 $18 SET DEC 6 SET SEX 1 .SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? Y $14 2) Number of animals ? Y $14 3) Percentages ? Y $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? N $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $14 EXACT cg,rci SET SEX 0 .SET TREND $1 Include Trend statistic ? Y $1 $1 0 1 5 25 $1 .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y

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$13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? N $13 13) Quartile range ? N $13 14) Trend Test 1)RoeLee 2)Jonckeere 1 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $13 16) Missing Values ? N $13 KWALL .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 ONEWAY SET STRATA SEX $2 Strata: F2 $2 Sex $2 $2 + PETO OPTIONS CHANGED - REMOVE CI'S AND RR OVER STRATA, JSF 25.11.91 .SET CHISQ $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? Y $11 2) Expected Positive values ? Y $11 3) Expected values compared with control ? Y $11 4) Number of animals ? Y $11 5) Mortality Ratio ? Y $11 6) Relative Risk ? Y $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Observations 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print 1) all fatal then inci 2) combined 3) fatal, inci1 $11 $11 CHISQ + *** REPEAT WITHOUT YATES CORRECTION .SET HEAD $136 7 :C:Without Yates correction .SET CHISQ $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? N $11 2) Expected Positive values ? N $11 3) Expected values compared with control ? N $11 4) Number of animals ? N $11 5) Mortality Ratio ? N

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$11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction 1)2x2 Tables 2)No 3)Trend also: 2 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Observations 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print 1) all fatal then inci 2) combined 3) fatal, inci1 $11 $11 &CHI + + reset Yates correction .SET HEAD $136 7 :L: .SET CHISQ $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? Y $11 2) Expected Positive values ? Y $11 3) Expected values compared with control ? Y $11 4) Number of animals ? Y $11 5) Mortality Ratio ? Y $11 6) Relative Risk ? Y $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Observations 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print 1) all fatal then inci 2) combined 3) fatal, inci1 $11 $11 SET TIME WOD PETO SET PO LI TUCOUNT * 1 CALC W5=%MAX(*5) NAME W5 "primary liver tumours" NAME /GRADE W5 3 .SET OBS $4 Treat observations in PETO $4 $4 1) Obsns: 1)Fatal 2)Incidental 3)Both 3 $4 2) Fatality Condn: W5 3 AND MOD <3 $4 3) Print both fatal and incidental results ? Y $4 $4 CALC W3=(WOD+4)/5 .SET TIME2 $20 Variable for grouped time of death: W3 $20 Work 3 $20 $20 INDEX WOD SET SEX 3 .SET LIST $31 List Fields options $31 $31 1) Include heading ? Y $31 2) Change character codes to numeric equivalents ? Y $31 LIST WOD,MOD,W3,CG,RCI,W5 SET SEX 0

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PETO W5 SET STRATA 0 SET PARTITION SEX SPEARMAN SODIUM,POTASS PEARSON SET STRATA 0 SET PARTITION SEX SET CUTS SODIUM 145 EXACT SODIUM KWSTRATA CALC W6=WOD FOR CG =0 CALC W6 = 0 FOR CG <0 CALC W6 = -1 FOR NAME W6 "Liver: congestion" VISIBLE W6 WRITE ITSTATS1

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Appendix 3B

Results from TSTATS1.CMD

Appendix 3B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test + *** table generated : 24-FEB-95, 15:00:07 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 1 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 1 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F60 Liver:congestion F61 Liver:RCI in portal tracts and/or sinusoids Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 3B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Fisher's Exact options 1) Number of Positive values ? Y 2) Number of animals ? Y 3) Percentages ? Y 4) Print probabilities ? Y 5) Minimum total positive ( or negative): 0 6) Repeat analyses from maximum cut of: 0 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 8) Show totals over partitions ? Y 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 10) Ahner-Passing Statistic ? N 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0

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Appendix 3B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Male Group Group Group Group 1 2 3 4 Control Low Middle High Trend Liver congestion n 1 0 2 3 N 10 10 10 10 %10.000000 0.000000 20.000000 30.000000 P 1.000000 1.000000 0.582043 0.115424 Liver RCI in portal tracts n 6 4 3 7 and/or sinusoids N 10 10 10 10 %60.000000 40.000000 30.000000 70.000000 P 0.656282 0.369850 1.000000 0.256596 1

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Appendix 3B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis + *** table generated : 24-FEB-95, 15:00:08 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 2 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F60 Liver:congestion F61 Liver:RCI in portal tracts and/or sinusoids Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 3B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Kruskal-Wallis/Fry-Lee options 1) Number of animals ? Y 2) Mean Ranks ? Y 3) Median Values ? Y 4) Confidence levels for Medians (give prob level): 0 5) Range (Minimum,Maximum) ? Y 6) Kruskal-Wallis statistic ? Y 7) Print probabilities ? Y 8) Print exact probabilities for comparisons ? Y 9) Yates correction ? Y 10) Minimum total outside one rank: 0 11) Show totals over partitions ? Y 12) Quantiles ? N 13) Quartile range ? N 14) Trend Test 1)RoeLee 2)Jonckheere 1 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 16) Missing Values ? N

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Appendix 3B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend Liver congestion N 20 20 20 20 80 MRank41.100000 36.950000 38.475000 45.475000 40.500000 Median0.000000 0.000000 0.000000 0.000000 0.000000 Min 0 0 0 0 0 Max 4 2 1 4 4 ChiSq 0.797555 0.283119 0.586268 3.348067 2.388871 P 0.371825 0.594664 0.443866 0.341009 0.122202 ExP 1.000000 1.000000 1.000000 Liver RCI in portal tracts N 20 20 20 20 80 and/or sinusoids MRank37.825000 35.200000 36.100000 52.875000 40.500000 Median0.000000 0.000000 0.000000 1.000000 0.500000 Min 0 0 0 0 0 Max 2 2 2 3 3 ChiSq 0.173847 0.076471 4.854828 9.307258 8.678411 P 0.676715 0.782139 0.027569 0.025473 0.003220 ExP 1.000000 1.000000 0.027431 2

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Appendix 3B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance + *** table generated : 24-FEB-95, 15:00:09 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 3 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F60 Liver:congestion F61 Liver:RCI in portal tracts and/or sinusoids Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0

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Appendix 3B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Number of decimal places: 6 One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? N 10) Harmonic Mean Values ? N 11) Coefficient of variation ? N 12) Relative Group Mean difference ? N 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 15) Degrees of freedom ? N 16) Number of contrasts: 0

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Appendix 3B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend Liver congestion N 20 20 20 20 80 Mean 0.400000 0.150000 0.150000 0.650000 0.337500 St.Err0.222427 0.109424 0.081918 0.264326 0.094037 St.Dev0.994723 0.489360 0.366348 1.182103 0.841093 Var P 0.003304 0.000062 0.458905 0.000001 F 0.905624 0.905624 0.905624 1.660311 3.155354 P 0.344295 0.344295 0.344295 0.182657 0.079680 Liver RCI in portal tracts N 20 20 20 20 80 and/or sinusoids Mean 0.550000 0.450000 0.500000 1.250000 0.687500 St.Err0.153469 0.135239 0.153897 0.239242 0.093446 St.Dev0.686333 0.604805 0.688247 1.069924 0.835809 Var P 0.586927 0.990439 0.060063 0.050857 F 0.162915 0.040729 7.982851 4.636299 13.175033 P 0.687620 0.840601 0.006030 0.004960 0.000512 3

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Appendix 3B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis + *** table generated : 24-FEB-95, 15:00:10 Table number of next output: (0 for none) 4 Page numbers 1) First Page number: (0 for none) 4 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F60 Liver:congestion F61 Liver:RCI in portal tracts and/or sinusoids Partition: Strata: F2 Sex Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001

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Appendix 3B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? Y 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? Y 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 18) Fatality Condn: 19) Print fatal(F) and incidental(I): 1

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Appendix 3B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Stratified by Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend Liver congestion n 4 2 3 6 15 E 3.750000 3.750000 3.750000 3.750000 15.000000 E(2) 3.000000 3.500000 5.000000 N 20 20 20 20 80 n/E1.066667 0.533333 0.800000 1.600000 RR 0.411765 0.714286 1.714286 ChiSq 0.202128 0.000000 0.128378 2.826087 2.025219 P 0.653009 1.000000 0.720119 0.419224 0.154707 Liver RCI in portal n 9 8 8 15 40 tracts and/or E10.000000 10.000000 10.000000 10.000000 40.000000 sinusoids E(2) 8.500000 8.500000 12.000000 N 20 20 20 20 80 n/E0.900000 0.800000 0.800000 1.500000 RR 0.814815 0.824561 3.500000 ChiSq 0.000000 0.000000 2.500000 6.630000 6.061972 P 1.000000 1.000000 0.113846 0.084674 0.013812 Without Yates correction Liver: congestion ChiSq 0.808511 0.165217 0.513514 2.826087 2.025219 P 0.368561 0.684398 0.473622 0.419224 0.154707 Liver: RCI in portal tracts and/or sinusoids ChiSq 0.099476 0.097436 3.600000 6.630000 6.061972 P 0.752459 0.754929 0.057780 0.084674 0.013812 4

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Appendix 3B - Table 5 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis by Peto Method + *** table generated : 24-FEB-95, 15:00:12 Table number of next output: (0 for none) 5 Page numbers 1) First Page number: (0 for none) 5 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F60 Liver:congestion F61 Liver:RCI in portal tracts and/or sinusoids Partition: Strata: F2 Sex Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001

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Appendix 3B - Table 5 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis by Peto Method Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Set time of death variable: F35 week of death Set decedents variable: Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? Y 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? Y 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 18) Fatality Condn: 19) Print fatal(F) and incidental(I): 1

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Appendix 3B - Table 5 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis by Peto Method Stratified by Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend Liver congestion n 4 2 3 6 15 E 3.545402 4.003018 3.913475 3.538104 15.000000 E(2) 3.139061 3.676316 5.048089 N 20 20 20 20 80 n/E1.128222 0.499623 0.766582 1.695823 RR 0.440713 0.676312 1.474478 ChiSq 0.273818 0.017865 0.082311 3.018380 2.068842 P 0.600782 0.893672 0.774190 0.388800 0.150336 Liver RCI in portal n 9 8 8 15 40 tracts and/or E 9.388061 10.856913 10.988050 8.766977 40.000000 sinusoids E(2) 9.111235 9.219507 11.489586 N 20 20 20 20 80 n/E0.958664 0.736858 0.728064 1.710966 RR 0.692300 0.665722 2.355712 ChiSq 0.117447 0.151476 2.041825 8.199250 6.948644 P 0.731820 0.697129 0.153026 0.042068 0.008388 5

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Appendix 3B - Table 6 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List + *** table generated : 24-FEB-95, 15:00:13 Table number of next output: (0 for none) 6 Page numbers 1) First Page number: (0 for none) 6 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 3 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F35 week of death F36 mode of death F158 Work 3 F60 Liver:congestion F61 Liver:RCI in portal tracts and/or sinusoids F159 primary liver tumours List Fields options 1) Include heading ? Y 2) Change character codes to numeric equivalents ? Y

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Appendix 3B - Table 6 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Male WOD |MOD|W3 |CG |RCI|W5 | 43 28 1 6 0 0 0 64 39 1 8 4 0 0 9 54 2 11 0 0 0 61 54 2 11 2 0 0 48 55 4 11 0 0 0 22 66 2 14 0 1 0 65 67 2 14 0 1 0 4 72 2 15 0 1 0 68 80 1 16 2 3 3 3 87 2 18 1 0 0 25 92 2 19 0 0 3 45 95 1 19 1 1 0 26 99 2 20 0 0 0 66 100 2 20 0 2 3 70 101 2 21 0 3 1 7 102 2 21 0 1 0 1 103 2 21 0 1 0 27 103 2 21 0 0 0 2 104 3 21 0 1 0 30 104 3 21 0 0 0 46 104 3 21 0 1 0 69 104 3 21 0 0 0 67 104 3 21 0 3 3 62 104 3 21 0 1 0 63 104 3 21 0 1 0 50 104 3 21 0 0 0 49 104 3 21 0 0 0 47 104 3 21 0 1 0 44 104 3 21 0 0 0 42 104 3 21 1 0 0 41 104 3 21 0 0 0 29 104 3 21 0 0 0 24 104 3 21 0 2 0 23 104 3 21 0 1 0 21 104 3 21 0 1 0 6 104 3 21 0 2 0 28 104 3 21 0 0 0 10 104 3 21 0 2 0 8 104 3 21 0 0 0 5 104 3 21 0 0 0 6

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Appendix 3B - Table 6 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Female WOD |MOD|W3 |CG |RCI|W5 | 14 19 1 4 1 0 0 32 40 1 8 1 0 0 77 43 2 9 0 1 0 17 59 1 12 2 0 0 13 68 2 14 0 1 0 40 71 1 15 0 1 0 76 77 1 16 1 1 1 34 83 2 17 0 0 0 56 87 2 18 0 1 0 51 87 2 18 0 0 0 12 89 1 18 4 1 0 80 90 2 18 0 2 0 54 91 2 19 0 0 0 19 93 2 19 0 0 0 79 96 2 20 3 3 1 73 99 2 20 0 0 0 58 100 2 20 0 1 0 37 101 1 21 2 0 0 59 103 2 21 0 0 0 38 104 3 21 0 0 0 78 104 3 21 0 1 1 74 104 3 21 1 1 1 75 104 3 21 0 1 3 72 104 3 21 0 0 3 71 104 3 21 0 1 0 60 104 3 21 0 2 1 52 104 3 21 0 1 0 57 104 3 21 0 2 0 55 104 3 21 0 0 1 53 104 3 21 1 0 0 39 104 3 21 0 0 0 36 104 3 21 0 1 0 35 104 3 21 0 1 0 33 104 3 21 0 1 0 31 104 3 21 0 0 0 11 104 3 21 0 0 0 15 104 3 21 0 0 0 18 104 3 21 0 0 0 20 104 3 21 0 1 0 16 104 3 21 0 0 0 7

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Appendix 3B - Table 7 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis by Peto Method + *** table generated : 24-FEB-95, 15:00:14 Table number of next output: (0 for none) 7 Page numbers 1) First Page number: (0 for none) 8 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F159 primary liver tumours Partition: Strata: F2 Sex Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001

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Appendix 3B - Table 7 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis by Peto Method Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Set time of death variable: F35 week of death Set decedents variable: Variable for grouped time of death: W3 Work 3 Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? Y 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? Y 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 3 18) Fatality Condn:W5 3 AND MOD <3 19) Print fatal(F) and incidental(I): 1

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Appendix 3B - Table 7 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis by Peto Method Stratified by Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend primary liver tumours FATAL n 0 1 0 2 3 E 0.742593 0.840509 0.775926 0.640972 3.000000 E(2) 0.562500 0.000000 0.928205 N 20 20 20 20 80 n/E0.000000 1.189755 0.000000 3.120260 RR ChiSq 0.015873 0.000000 0.657304 4.430936 3.301383 P 0.899741 1.000000 0.417513 0.218534 0.069222 INCIDENTAL n 0 0 2 8 10 E 1.842809 2.364549 2.437012 3.355630 10.000000 E(2) 0.000000 1.090909 4.833333 N 20 19 20 18 77 n/E0.000000 0.000000 0.820677 2.384053 RR ChiSq 0.000000 0.375000 6.414579 18.647961 18.156421 P 1.000000 0.540291 0.011319 0.000323 0.000020 TOTAL n 0 1 2 10 13 E 2.585402 3.205058 3.212938 3.996602 13.000000 E(2) 0.562500 1.090909 5.761538 N 20 20 20 20 80 n/E0.000000 0.312007 0.622483 2.502126 RR ChiSq 0.015873 0.375000 8.702450 20.948401 20.889903 P 0.899741 0.540291 0.003178 0.000108 0.000005 8

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Appendix 3B - Table 8 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Spearman Correlations + *** table generated : 24-FEB-95, 15:00:15 Table number of next output: (0 for none) 8 Page numbers 1) First Page number: (0 for none) 9 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79 Sodium at 6 months (mmol/l) F80 Potassium at 6 months (mmol/l) Partition: F2 Sex Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 3B - Table 8 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Spearman Correlations Partitioned on Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total correlated with Sodium at 6 months (mmol/l) Potassium at 6 months (mmol/ l) Male N 10 10 10 10 40 r-0.757576 -0.139394 0.510641 0.261399 0.148174 P 0.023043 0.675814 0.125542 0.432924 0.354785 Female N 9 10 10 10 39 r-0.341775 0.903030 0.376901 -0.187879 0.427978 P 0.333701 0.006747 0.258180 0.573002 0.008334 9

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Appendix 3B - Table 9 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Pearson Correlations + *** table generated : 24-FEB-95, 15:00:15 Table number of next output: (0 for none) 9 Page numbers 1) First Page number: (0 for none) 10 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79 Sodium at 6 months (mmol/l) F80 Potassium at 6 months (mmol/l) Partition: F2 Sex Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 3B - Table 9 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Pearson Correlations Partitioned on Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total correlated with Sodium at 6 months (mmol/l) Potassium at 6 months (mmol/ l) Male N 10 10 10 10 40 r-0.740965 0.023398 0.383982 0.514713 0.185746 P 0.014211 0.948846 0.273313 0.127934 0.251162 Female N 9 10 10 10 39 r-0.434687 0.714868 0.482202 -0.376101 0.534596 P 0.242316 0.020151 0.158125 0.284110 0.000455 10

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Appendix 3B - Table 10 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test + *** table generated : 24-FEB-95, 15:00:16 Table number of next output: (0 for none) 10 Page numbers 1) First Page number: (0 for none) 11 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(145) Sodium at 6 months (mmol/l) Partition: F2 Sex Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 3B - Table 10 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Fisher's Exact options 1) Number of Positive values ? Y 2) Number of animals ? Y 3) Percentages ? Y 4) Print probabilities ? Y 5) Minimum total positive ( or negative): 0 6) Repeat analyses from maximum cut of: 0 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 8) Show totals over partitions ? Y 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 10) Ahner-Passing Statistic ? N 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0

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Appendix 3B - Table 10 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Partitioned on Sex Group Group Group Group 1 2 3 4 Control Low Middle High Trend Sodium at 6 months (mmol/l) ( > 145 ) Male n 10 6 7 2 N 10 10 10 10 100.000000 60.000000 70.000000 20.000000 P 0.086687 0.210526 0.000714 0.001011 Female n 7 3 7 9 N 9 10 10 10 %77.777778 30.000000 70.000000 90.000000 P 0.102514 1.000000 0.916409 0.058246 TOTAL n 17 9 14 11 N 19 20 20 20 %89.473684 45.000000 70.000000 55.000000 P 0.006759 0.279534 0.029555 11

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Appendix 3B - Table 11 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fry-Lee Stratified Rank Test + *** table generated : 24-FEB-95, 15:00:17 Table number of next output: (0 for none) 11 Page numbers 1) First Page number: (0 for none) 12 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(145) Sodium at 6 months (mmol/l) Partition: F2 Sex Strata: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001

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Appendix 3B - Table 11 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fry-Lee Stratified Rank Test Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Kruskal-Wallis/Fry-Lee options 1) Number of animals ? Y 2) Mean Ranks ? Y 3) Median Values ? Y 4) Confidence levels for Medians (give prob level): 0 5) Range (Minimum,Maximum) ? Y 6) Kruskal-Wallis statistic ? Y 7) Print probabilities ? Y 8) Print exact probabilities for comparisons ? Y 9) Yates correction ? Y 10) Minimum total outside one rank: 0 11) Show totals over partitions ? Y 12) Quantiles ? N 13) Quartile range ? N 14) Trend Test 1)RoeLee 2)Jonckheere 1 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 16) Missing Values ? N

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Appendix 3B - Table 11 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fry-Lee Stratified Rank Test Partitioned on Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend Sodium at 6 months (mmol/l) Male N 10 10 10 10 40 ORank16.825000 9.025000 10.125000 5.025000 10.250000 D 6.575000 -1.225000 -0.125000 -5.225000 0.000000 ChiSq 7.822857 6.811672 11.580135 21.094989 12.509809 P 0.005159 0.009056 0.000667 0.000101 0.000405 ExP 0.000725 0.001624 0.000011 Female N 9 10 10 10 39 ORank 8.410256 5.743590 11.871795 13.974359 10.000000 D -0.820513 -4.512821 1.615385 3.717949 0.000000 ChiSq 2.472586 0.511763 3.159293 10.986713 6.736850 P 0.115847 0.474376 0.075496 0.011798 0.009444 ExP 0.050553 1.000000 0.029293 TOTAL N 19 20 20 20 79 ORank25.235256 14.768590 21.996795 18.999359 20.250000 D 5.754487 -5.737821 1.490385 -1.507051 0.000000 ChiSq 11.366651 1.208979 0.858585 10.580692 0.464286 P 0.000748 0.271534 0.354135 0.014223 0.495628 12

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Appendix 3B - Table 12 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Visible tumour analysis by Peto Method + *** table generated : 24-FEB-95, 15:00:20 Table number of next output: (0 for none) 12 Page numbers 1) First Page number: (0 for none) 13 2) Page number: 1)Top or 2)Bottom 2 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 1 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F160 Liver: congestion Partition: F2 Sex Strata: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001

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Appendix 3B - Table 12 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Visible tumour analysis by Peto Method Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Set time of death variable: F35 week of death Set decedents variable: Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? Y 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? Y 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 3 18) Fatality Condn:W5 3 AND MOD <3 19) Print fatal(F) and incidental(I): 1

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Appendix 3B - Table 12 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Visible tumour analysis by Peto Method Partitioned on Sex Group Group Group Group 1 2 3 4 Control Low Middle High Total Trend Liver: congestion Male n 1 0 2 3 6 E 1.496285 1.639730 1.569720 1.294265 6.000000 E(2) 0.529412 1.616667 1.868922 N 10 10 10 10 40 n/E0.668322 0.000000 1.274113 2.317917 RR 0.000000 1.816027 3.976102 ChiSq 0.003472 0.018345 0.401028 4.177679 3.346890 P 0.953011 0.892261 0.526559 0.242906 0.067332 Female n 3 2 1 3 9 E 2.049118 2.363288 2.343756 2.243839 9.000000 E(2) 2.609649 2.059649 3.179167 N 10 10 10 10 40 n/E1.464045 0.846279 0.426666 1.336995 RR 0.616811 0.302559 0.837317 ChiSq 0.009677 0.313773 0.069174 1.540727 0.154514 P 0.921635 0.575374 0.792543 0.672903 0.694258 TOTAL n 4 2 3 6 15 E 3.545402 4.003018 3.913475 3.538104 15.000000 E(2) 3.139061 3.676316 5.048089 N 20 20 20 20 80 n/E1.128222 0.499623 0.766582 1.695823 RR 0.440713 0.676312 1.474478 ChiSq 0.273818 0.017865 0.082311 3.018380 2.068842 P 0.600782 0.893672 0.774190 0.388800 0.150336

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Appendix 4A Command file TONEWAY.CMD

+ *** + *** Command File TONEWAY.CMD + *** Used to test DATATOX F1 Statistics + *** Parametric Statistics - + *** Mean + *** St. Error + *** St. Deviation + *** Geometric Mean + *** Harmonic Mean + *** Coefficient of Variation + *** Relative Group Mean difference + *** T-tests 1) Using overall root-mean Square + *** 2) 2-group comparions + *** 3) Welch Test + *** 4) Fisher-Pitman test + *** Adjustments 1) Dunnett's + *** 2-5) Various Bonferronni Tests + *** Trend test via Cochran-Armitage + *** Variance Tests 1)Bartlett 2)Levene + *** Totals via F-test + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SEX 1 SELECT SET SEX 0 +SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 SET FACTOR GROUP .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 4B - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry

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$36 4 :C: $36 5 :C: $36 6 :COMales $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation $36 $36 further heading for group comparison analyses $36 11:L: $36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm $36 14TB: T T T T $36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 + + *** MALES ONLY FOR SEX 1 .SET HEAD $136 6 :COMales $136 7 :COT-test via RoeLee method .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N

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$12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb2 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY .SET onew $112 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb3 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb4 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb5 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? y $112 8) Print probabilities ? y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $112 15) Degrees of freedom ? Y &ONEWAY .SET HEAD $136 7 :COT-test via Welch method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 3 &ONEWAY .SET HEAD $136 7 :COT-test via Pitman method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 4 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? Y $112 8) Print probabilities ? Y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 15) Degrees of freedom ? N &ONEWAY /LUDIN &ONEWAY /LUDIN =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &ONEWAY .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &ONEWAY + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1

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$18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + *** REPEAT ABOVE TESTS FOR FEMALES .SET HEAD $136 6 :COFemales $136 7 :COT-test via RoeLee method FOR SEX 2 .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb2 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY .SET onew $112 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb3 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb4 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb5 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? y $112 8) Print probabilities ? y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $112 15) Degrees of freedom ? Y &ONEWAY .SET HEAD $136 7 :COT-test via Welch method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 3

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&ONEWAY .SET HEAD $136 7 :COT-test via Pitman method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 4 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? Y $112 8) Print probabilities ? Y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 15) Degrees of freedom ? N &ONEWAY /LUDIN &ONEWAY /LUDIN =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &ONEWAY .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &ONEWAY + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + *** REPEAT ABOVE TESTS FOR ALL .SET HEAD $136 6 :COMales and Females $136 7 :COT-test via RoeLee method FOR .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n

ROELEE 3.1 138

$12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb2 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY .SET onew $112 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb3 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb4 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb5 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? y $112 8) Print probabilities ? y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $112 15) Degrees of freedom ? Y &ONEWAY .SET HEAD $136 7 :COT-test via Welch method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 3 &ONEWAY .SET HEAD $136 7 :COT-test via Pitman method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 4 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? Y $112 8) Print probabilities ? Y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 15) Degrees of freedom ? N &ONEWAY /LUDIN &ONEWAY /LUDIN =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &ONEWAY .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &ONEWAY + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0

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$18 .SET HEAD $136 9 :C: + *** repeat for ALL with partition SEX FOR .SET HEAD $136 6 :COMales and Females $136 7 :COT-test via RoeLee method SET PART SEX .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb2 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY .SET onew $112 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb3 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb4 &ONEWAY .SET onew $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb5 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? y $112 8) Print probabilities ? y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $112 15) Degrees of freedom ? Y &ONEWAY .SET HEAD $136 7 :COT-test via Welch method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 3 &ONEWAY .SET HEAD

ROELEE 3.1 140

$136 7 :COT-test via Pitman method .SET onew $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 4 &ONEWAY .SET HEAD $136 7 :COT-test via 2-group method .SET onew $112 7) F statistic ? Y $112 8) Print probabilities ? Y $112 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 2 $112 15) Degrees of freedom ? N &ONEWAY /LUDIN &ONEWAY /LUDIN =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &ONEWAY .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &ONEWAY + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: WRITE ITONEWAY

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Appendix 4B

Results from TONEWAY.CMD Appendix 4B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males T-test via RoeLee method + *** table generated : 24-FEB-95, 15:01:35 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 1 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 1 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Male Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 4B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males T-test via RoeLee method One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

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1 Appendix 4B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males T-test via RoeLee method Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 N 10 10 10 10 40 months (mmol/ Mean 150.020000 144.940000 145.490000 142.870000 145.830000 l) GMean 150.010972 144.895886 145.443061 142.845482 145.775537 HMean 150.001988 144.851332 145.395380 142.820376 145.720509 St.Err 0.549909 1.186142 1.222152 0.871914 0.634956 St.Dev 1.738965 3.750911 3.864784 2.757233 4.015815 Var P 0.031708 0.026099 0.185860 0.114570 CoefV 1.159156 2.587906 2.656392 1.929889 2.753765 %dev -3.386215 -3.019597 -4.766031 F 13.022939 10.355665 25.798452 9.159348 14.413788 df 36 36 36 36 36 P 0.000928 0.002731 0.000012 0.000122 0.000543 Dun P 0.002621 0.007566 0.000035 Lev P 0.165494 0.137782 0.879784 0.256734 B1 P 0.010000 0.010000 0.000035 B2 P 0.010000 0.010000 0.001000 B3 P 0.010000 0.010000 0.001000 B4 P 0.010000 0.010000 0.001000 T-test via 2-group method F 15.097348 11.425537 48.109257 9.159348 14.413788 df 18 18 18 36 36 P 0.001084 0.003335 0.000002 0.000122 0.000543 T-test via Welch method F 15.097348 11.425537 48.109257 9.159348 14.413788 df 13 13 15 36 36 P 0.001877 0.004927 0.000005 0.000122 0.000543 T-test via Pitman method F 15.097348 11.425537 48.109257 9.159348 14.413788 df 36 36 P 0.000455 0.000877 0.000011 0.000122 0.000543 T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 F 14.413788 F 4.845035 F 15.097348 F P 0.000543 P 0.036457 P 0.001084 P

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2 Appendix 4B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.001000 F 14.413788 F 4.845035 F 15.097348 11.425537 7.279107 P 0.000543 P 0.036457 P 0.001084 0.003335 0.002962 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend F 15.097348 11.425537 7.279107 4.845035 P 0.001084 0.003335 0.002962 0.036457 Groups 3 and 4 removed F 15.097348 15.097348 15.097348 P 0.001084 0.001084 0.001084

ROELEE 3.1 145

Appendix 4B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females T-test via RoeLee method + *** table generated : 24-FEB-95, 15:01:55 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 3 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 2 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Female Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

ROELEE 3.1 146

Appendix 4B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females T-test via RoeLee method One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

ROELEE 3.1 147

3 Appendix 4B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females T-test via RoeLee method Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 N 9 10 10 10 39 months (mmol/ Mean 145.644444 141.480000 144.690000 147.440000 144.792308 l) GMean 145.640452 141.371465 144.556446 147.429239 144.709346 HMean 145.636464 141.258390 144.418362 147.418456 144.622625 St.Err 0.381558 1.810021 2.037070 0.593146 0.777955 St.Dev 1.144674 5.723791 6.441782 1.875692 4.858329 Var P 0.000127 0.000052 0.179023 0.000011 CoefV 0.785937 4.045653 4.452127 1.272173 3.355378 %dev -2.859323 -0.655325 1.232835 F 4.046920 0.212575 0.752330 3.061807 4.736273 df 35 35 35 35 35 P 0.052001 0.647609 0.391648 0.040758 0.036368 Dun P 0.126313 0.937007 0.713423 Lev P 0.191224 0.000087 0.062374 0.002818 B1 P 1.000000 1.000000 1.000000 B2 P 1.000000 1.000000 1.000000 B3 P 1.000000 1.000000 1.000000 B4 P 1.000000 1.000000 1.000000 T-test via 2-group method F 4.573733 0.191057 6.159946 3.061807 4.736273 df 17 17 17 35 35 P 0.047277 0.667540 0.023812 0.040758 0.036368 T-test via Welch method F 5.068320 0.212087 6.481632 3.061807 4.736273 df 10 10 15 35 35 P 0.048074 0.654989 0.022379 0.040758 0.036368 T-test via Pitman method F 4.573733 0.191057 6.159946 3.061807 4.736273 df 35 35 P 0.015285 1.000000 0.026283 0.040758 0.036368 T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 F 4.736273 F 0.077139 F 4.573733 0.191057 1.765368 P 0.036368 P 0.783410 P 0.047277 0.667540 0.191024

ROELEE 3.1 148

4 Appendix 4B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.001000 F 4.736273 F 4.573733 0.191057 6.159946 3.061807 P 0.036368 P 0.047277 0.667540 0.023812 0.040758 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend F 4.573733 0.191057 1.765368 0.077139 P 0.047277 0.667540 0.191024 0.783410 Groups 3 and 4 removed F 4.573733 4.573733 4.573733 P 0.047277 0.047277 0.047277

ROELEE 3.1 149

Appendix 4B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via RoeLee method + *** table generated : 24-FEB-95, 15:02:19 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 5 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

ROELEE 3.1 150

Appendix 4B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via RoeLee method One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

ROELEE 3.1 151

5 Appendix 4B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via RoeLee method Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 N 19 20 20 20 79 months (mmol/ Mean 147.947368 143.210000 145.090000 145.155000 145.317722 l) GMean 147.924613 143.122827 144.999076 145.119264 145.248211 HMean 147.901941 143.032301 144.905224 145.082993 145.176440 St.Err 0.612700 1.125468 1.159739 0.733610 0.501076 St.Dev 2.670699 5.033247 5.186511 3.280801 4.453658 Var P 0.009625 0.006857 0.387617 0.013558 CoefV 1.805168 3.514592 3.574685 2.260206 3.064773 %dev -3.202063 -1.931341 -1.887407 F 12.374555 4.501816 4.299329 4.183898 0.148515 df 75 75 75 75 75 P 0.000743 0.037162 0.041562 0.008558 0.701050 Dun P 0.002121 0.093766 0.104125 Lev P 0.186617 0.040225 0.955180 0.114956 B1 P 0.010000 1.000000 1.000000 B2 P 0.010000 0.100000 0.100000 B3 P 0.010000 0.050000 0.050000 B4 P 0.010000 0.050000 0.050000 T-test via 2-group method F 13.269690 4.602805 8.444160 4.183898 0.148515 df 37 37 37 75 75 P 0.000822 0.038550 0.006151 0.008558 0.701050 T-test via Welch method F 13.667209 4.745740 8.534866 4.183898 0.148515 df 29 29 36 75 75 P 0.000905 0.037644 0.005983 0.008558 0.701050 T-test via Pitman method F 13.269690 4.602805 8.444160 4.183898 0.148515 df 37 37 37 75 75 P 0.000822 0.038550 0.006151 0.008558 0.701050 T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 F 0.148515 F 13.269690 4.602805 8.444160 4.183898 P 0.701050 P 0.000822 0.038550 0.006151 0.008558

ROELEE 3.1 152

6 Appendix 4B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.001000 F 0.148515 F 13.269690 4.602805 8.444160 4.183898 P 0.701050 P 0.000822 0.038550 0.006151 0.008558 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend F 13.269690 4.602805 5.523271 0.926865 P 0.000822 0.038550 0.006467 0.339818 Groups 3 and 4 removed F 13.269690 13.269690 13.269690 P 0.000822 0.000822 0.000822

ROELEE 3.1 153

Appendix 4B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via RoeLee method + *** table generated : 24-FEB-95, 15:02:27 Table number of next output: (0 for none) 4 Page numbers 1) First Page number: (0 for none) 7 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: F2 Sex Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 4B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via RoeLee method One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

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7 Appendix 4B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via RoeLee method Partitioned on Sex Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 months (mmol/l) Male N 10 10 10 10 40 Mean 150.020000 144.940000 145.490000 142.870000 145.830000 GMean 150.010972 144.895886 145.443061 142.845482 145.775537 HMean 150.001988 144.851332 145.395380 142.820376 145.720509 St.Err 0.549909 1.186142 1.222152 0.871914 0.634956 St.Dev 1.738965 3.750911 3.864784 2.757233 4.015815 Var P 0.031708 0.026099 0.185860 0.114570 CoefV 1.159156 2.587906 2.656392 1.929889 2.753765 %dev -3.386215 -3.019597 -4.766031 F 13.022939 10.355665 25.798452 9.159348 14.413788 df 36 36 36 36 36 P 0.000928 0.002731 0.000012 0.000122 0.000543 Dun P 0.002621 0.007566 0.000035 Female N 9 10 10 10 39 Mean 145.644444 141.480000 144.690000 147.440000 144.792308 GMean 145.640452 141.371465 144.556446 147.429239 144.709346 HMean 145.636464 141.258390 144.418362 147.418456 144.622625 St.Err 0.381558 1.810021 2.037070 0.593146 0.777955 St.Dev 1.144674 5.723791 6.441782 1.875692 4.858329 Var P 0.000127 0.000052 0.179023 0.000011 CoefV 0.785937 4.045653 4.452127 1.272173 3.355378 %dev -2.859323 -0.655325 1.232835 F 4.046920 0.212575 0.752330 3.061807 4.736273 df 35 35 35 35 35 P 0.052001 0.647609 0.391648 0.040758 0.036368 Dun P 0.126313 0.937007 0.713423 Male Lev P 0.165494 0.137782 0.879784 0.256734 B1 P 0.010000 0.010000 0.000035 Female Lev P 0.191224 0.000087 0.062374 0.002818 B1 P 1.000000 1.000000 1.000000 Male B2 P 0.010000 0.010000 0.001000 Female B2 P 1.000000 1.000000 1.000000 Male B3 P 0.010000 0.010000 0.001000 Female B3 P 1.000000 1.000000 1.000000 Male B4 P 0.010000 0.010000 0.001000 Female B4 P 1.000000 1.000000 1.000000 T-test via 2-group method Male F 15.097348 11.425537 48.109257 9.159348 14.413788 df 18 18 18 36 36 P 0.001084 0.003335 0.000002 0.000122 0.000543 Female F 4.573733 0.191057 6.159946 3.061807 4.736273 df 17 17 17 35 35 P 0.047277 0.667540 0.023812 0.040758 0.036368

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8 Appendix 4B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via Welch method Partitioned on Sex Control 1 ppm 5 ppm 25 ppm Total Trend Male F 15.097348 11.425537 48.109257 9.159348 14.413788 df 13 13 15 36 36 P 0.001877 0.004927 0.000005 0.000122 0.000543 Female F 5.068320 0.212087 6.481632 3.061807 4.736273 df 10 10 15 35 35 P 0.048074 0.654989 0.022379 0.040758 0.036368 T-test via Pitman method Male F 15.097348 11.425537 48.109257 9.159348 14.413788 df 36 36 P 0.000455 0.000877 0.000011 0.000122 0.000543 Female F 4.573733 0.191057 6.159946 3.061807 4.736273 df 35 35 P 0.015285 1.000000 0.026283 0.040758 0.036368 T-test via 2-group method Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 Male F 14.413788 F 4.845035 F 15.097348 P 0.000543 P 0.036457 P 0.001084 Ludin procedure with alpha set at 0.001000 Male F 14.413788 F 4.845035 F 15.097348 11.425537 7.279107 P 0.000543 P 0.036457 P 0.001084 0.003335 0.002962 Female F 4.736273 F 4.573733 0.191057 6.159946 3.061807 P 0.036368 P 0.047277 0.667540 0.023812 0.040758 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Male F 15.097348 11.425537 7.279107 4.845035 P 0.001084 0.003335 0.002962 0.036457 Female F 4.573733 0.191057 1.765368 0.077139 P 0.047277 0.667540 0.191024 0.783410

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9 Appendix 4B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females T-test via 2-group method Partitioned on Sex Groups 3 and 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Male F 15.097348 15.097348 15.097348 P 0.001084 0.001084 0.001084 Female F 4.573733 4.573733 4.573733 P 0.047277 0.047277 0.047277

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Appendix 4C

ExTrnd Routine SUBROUTINE ExTrnd(result, pres, flev, P, PDir 1 , Trend8, probmn, mode 1 , oPTr, scTrmx, mxscTr, nscTr1, scTr1, pscTr1) c c routine to calculate Exact Trend8 statistic for 2xflev at vecp and c group levels in 'factor' c vecp - pointer to variable c factor - vector holding group levels c flev - no. of levels c enaml - no. of animals c P - Probability reject c PDir - Direction of probability c oPTr - Partitioned trend wanted c rP2Tl - true if two tailed test wanted c mode - 0) from Fisher exact, 1) from KrWall for WMW exact P c c This algorithm can now be extended to c 2) Fisher-Pitman test c c result - >0 if error, or too many to calculate c pres - vector holding frequency of values at different scoring points c 1 - flev is number present, c flev+1 to 2*flev is number absent c flev - number of scroring positions c P - Probability c PDir - direction of prob c Trend8 - scores at the different positions, now real*4 c probmn - minimum probability of interest c c When no paritioned values of interest, sort the scores into order c so that the wanted prob found as fast as possible c when this prob exceeds probmn we know we can finish c c Algorithm cc 1 Find minimal legal starting position, filling pegs from left to right cc Calc Prob and score cc Put Prob into total prob, if >minimum P stop cc cc 2 IF Peg >1 STOP cc IF Peg < last peg & } Look for lowest legal moves form peg to cc counters on peg >0 } higher peg where score <= observed score cc if possible, do move, store new position cc against pegs from original to new position cc identify this peg cc go to 2 cc cc 3 identify next lower peg cc go to 2 include 'pmo.txt' parameter(maxprt=30) logical*1 revrse, invert 1 , oPTr, iPTr integer*2 pres(*) 1 , nscTr1(*) 1 , PDir 1 , abs(maxprt), grptot(maxprt), sorttr(maxprt) 1 , trgrp(maxprt), presx(maxprt, maxprt) 1 , absx(maxprt, maxprt) 1 , prs(maxprt) real*8 P, probmn 1 , XP, xprob(maxprt), probt, small 1 , P2T(2), escore, EstT, expp, obsp real*4 pscTr1(mxscTr,1) integer*4 scTr1(mxscTr,1), scTrmx real*8 Trend8(*)

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1 , oscore, xscore(maxprt), trscr(maxprt), xs, xsp 1 , TI, TN, tmpt equivalence (PageV(1,1), presx(1,1)) 1 , (Page(1), absx (1,1)) iPTr = oPTr ! used to mark when Partioned trend will not work result = 0 N=0 PDir = 0 jtail = rP2Tl ccc ! +1 for positive Trend8, -1 for negative Trend8 P = 1.0 small = DLOG(.1D-18) nscr = 0 flevs = flev if(mode.eq.0) flevs = flev +1 do 10 i=1, flev if((mode.eq.0).and.(rComp.eq.-4)) then ccc For normal exact, levels = group levels ccc ignore levels that have been marked as ignore if(rCompl(i).lt.0) go to 10 endif n = n +1 prs(n) = 0 abs(n) = 0 grptot(n) = 0 ccc ! sort Trend8 into descending order ccc ! put sorted order into sorttr I1 = N TN = Trend8(i) 20 I1 = I1-1 if(I1.gt.0) then NI = sorttr(I1) TI = Trend8(NI) if(TN.gt.TI) then sorttr(I1+1) = NI go to 20 endif endif sorttr(I1+1) = i 10 continue ngrp = 0 TI = 99.0E5 ccc ! find any ties, put trends after matching ties into trscr ccc ! ngrp is number of different scores for use do i=1, N i1 = sorttr(i) TN = Trend8(i1) if(TN.lt.TI) ngrp = ngrp + 1 TI = TN trgrp(i1) = ngrp trscr(ngrp) = TI enddo if(ngrp.le.1) then if(change.and.(mode.eq.0)) then call wrnE(2901) ! 'need more than one Trend8 group',a) endif result = 301 nscr = -1 go to 995 endif N = 0 prtot = 0 abstot = 0 ccc ! take results out of pres and put into prs and abs ccc ! totals for scores into grptot do 60 i=1, flev igp = trgrp(i) if(igp.le.0) go to 60 pr = pres(flevs+i) ab = pres(i)

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prs(igp) = prs(igp) + pr abs(igp) = abs(igp) + ab prtot = prtot + pr abstot = abstot + ab grptot(igp) = grptot(igp) + pr + ab N = N + pr + ab 60 continue 59 continue IF(N.lt.1) then go to 995 endif if(.not.oPTr .and.(prtot.gt.abstot)) then ccc ! reverse Trend8 ccc ! enables stopping at sooner point revrse = .true. jtail = -jtail do 70 i=1, ngrp temp = prs(i) prs(i) = abs(i) abs(i) = temp 70 continue temp = prtot prtot = abstot abstot = temp else revrse = .false. endif if(prtot.gt.10) then EstT = ((prtot-10)/3.0)*0.5 if(ngrp.gt.3) EstT = EstT*(DSQRT(DFLOAT(prtot))**(ngrp-3)) if( ((eMode.eq.1).and.(EstT.gt.60000)) .or. 1 ((eMode.le.0).and.(EstT.gt.1200)) ) then ccc allow 5 minutes in batch mode, or two minutes in interactive mode if(change.and.(mode.eq.0)) then call wrnE(2902) ccc 'too many observations for Trend8 to deal with',a) endif P = -2.0D0 result = 303 nscr = -1 go to 995 endif else if(prtot.le.0) then if(change.and.(mode.eq.0)) then call wrnE(2903) ! 'no positive obsns found',a) endif nscr = -1 go to 995 endif itail = 1 oscore = 0.0D0 ! oscore is observed score escore = 0.0D0 ! escore is expected score do 75 i=1, ngrp oscore = oscore + prs(i)*trscr(i) escore = escore + grptot(i)*trscr(i) 75 continue escore = escore*prtot/DFLOAT(N) invert = .false. if(oPTr.or.(oscore.lt.escore-xsmall) ) then ccc ! invert so that score is getting larger invert = .true. jtail = -jtail endif 80 continue if(invert .or. (itail.eq.2) ) then oscore = -oscore ng2 = (ngrp+1)/2 do 300 i=1, ng2 ni = ngrp +1-i if(ni.ne.i) then

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tmpp = prs(i) tmpa = abs(i) tmpg = grptot(i) tmpt = trscr(i) abs(i) = abs(ni) abs(ni) = tmpa prs(i) = prs(ni) prs(ni) = tmpp grptot(i) = grptot(ni) grptot(ni) = tmpg trscr(i) =-trscr(ni) trscr(ni) =-tmpt else trscr(i) =-trscr(i) endif 300 continue endif ccc find minimal legal starting position ix = 1 xs = 0 np = prtot ccc ! no. to be placed do 90 i=1, ngrp if(np.gt.0) then npi = min0(np, grptot(i)) presx(i,ix) = npi absx (i,ix) = grptot(i) - npi ixtop = i np = np - npi xs = xs + npi*trscr(i) else presx(i,ix) = 0 absx (i,ix) = grptot(i) endif 90 continue call calcp(xp,ngrp, ix, presx,grptot,prtot,N, maxprt) probt = 0.0D0 obsp = 0.0D0 if(xp.gt.small) then expp = DEXP(xp) if(oPTr) then if(nscr.lt.mxscTr) then nscr = nscr +1 scTr1(nscr,1) = -xs pscTr1(nscr,1) = expp if(xs-oscore.ge.-xsmall) probt = expp if(DABS(xs-oscore).lt.xsmall) obsp = expp else nscr = mxscTr +1 iPTr = .false. endif else probt = expp endif endif if(.not. oPTr .and.(probt.gt.probmn)) go to 900 do ix1 = 1, ixtop xscore(ix1) = xs xprob (ix1) = xp if(ix1.gt.1) then do i=1, ngrp presx(i,ix1) = presx(i,1) absx (i,ix1) = absx (i,1) enddo endif enddo peg = ixtop ccc ! start at highest peg with counters jscore = 0 jscore = jscore +1

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if(mode.eq.2) write(99,1099) 1 jscore,xs,oscore,peg,ipold,ip,(presx(j,peg),j=1,N) 1099 format(i4,2f10.2,3i3,20i2) 200 continue if(peg.le.0) go to 990 ccc ! stop if((peg.lt.ngrp) .and. (presx(peg,peg) .gt.0)) then ccc check if can move counter to a higher peg with score >= oscore ipold = peg ip = peg + 1 201 continue if(presx(ip,peg).ge.grptot(ip)) then ccc ! peg posn full ip = ip +1 if(ip.le.ngrp) go to 201 ccc ! try next higher peg peg = peg -1 go to 200 ccc ! try again from lower peg endif xs= xscore(peg) - trscr(ipold) + trscr(ip) if(oPTr) then if(xs.lt.-scTrmx-xsmall) then peg = peg -1 go to 200 endif else if(xs-oscore.lt.-xsmall) then ccc ! score too high peg = peg -1 go to 200 endif ccc move legal, do it and store against new peg, and ones in between jscore = jscore +1 if(mode.eq.2) write(99,1099) 1 jscore,xs,oscore,peg,ipold,ip,(presx(j,peg),j=1,N) pold = presx(ipold, peg) -1 pnew = presx(ip , peg) +1 aold = absx (ipold, peg) +1 anew = absx (ip , peg) -1 presx(ipold, peg) = pold presx(ip , peg) = pnew absx (ipold, peg) = aold absx (ip , peg) = anew xp = xprob(peg) xp = xp + DLOG((anew+1)/dfloat(aold)) 1 - DLOG(pnew/DFLOAT(pold+1)) if(xp.gt.small) then expp = DEXP(xp) if(oPTr) then if(nscr.lt.mxscTr) then ccc make sure stored scores are in order isc = 0 xsp = -xs 400 continue isc = isc +1 if(isc.gt.nscr) then else if(xsp.gt.scTr1(isc,1)) then go to 400 else if(xsp.eq.scTr1(isc,1)) then pscTr1(isc,1) = pscTr1(isc,1) + expp go to 430 else do 410 isci=nscr, isc, -1 scTr1(isci+1,1) = scTr1(isci,1) pscTr1(isci+1,1) = pscTr1(isci,1) 410 continue endif

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nscr = nscr +1 scTr1(isc,1) = xsp pscTr1(isc,1) = expp 430 continue else nscr = mxscTr +1 iPTr = .false. endif if((xs-oscore).ge.-xsmall) probt = probt + expp if(DABS(xs-oscore).lt.xsmall) obsp = obsp + expp else probt = probt + expp if(probt.gt.probmn) go to 900 endif endif xprob (peg) = xp xscore(peg) = xs do 202 ix1 = peg+1, ip if(ix1.eq.ngrp) go to 202 ccc ! dont bother storing highest peg poss do 210 i=1, ngrp presx(i, ix1) = presx(i, peg) absx (i, ix1) = absx (i, peg) 210 continue xscore(ix1) = xs xprob (ix1) = xp 202 continue ccc identify this next higher peg peg = ip go to 200 endif ccc identify next lower peg peg = peg -1 go to 200 900 continue Probt = .5 go to 990 990 continue if(oPTr) then P2T(1) = ProbT P2T(2) = 1.0D0 - ProbT + obsp else P2T(itail) = ProbT if(itail.lt.2) then itail = itail+1 if(Probt.gt.probmn) go to 80 P2T(itail) = 0.5D0 endif endif if(rP2Tl.eq.0) then P= 2.0D0*DMIN1(P2T(1), P2T(2), 0.5D0) else if(jtail.lt.0) jtail=2 P=P2T(jtail) endif if(P.lt.probmn) then if(P2T(1).lt.P2T(2)) then PDir = 1 else PDir = -1 endif if(revrse) PDir = -PDir if(invert) PDir = -PDir endif 995 continue if(nscr.gt.mxscTr) nscr = -1 ! mark that convolving impossible

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ccc ! JSF, 11.11.93 nscTr1(1) = nscr if(oPTr.and. .not.iPTr) then ccc ! partioned trend will be impossible oPTr = .false. endif RETURN END subroutine calcp(xp, ngrp, ix, presx, grptot, prtot, N, mxpart) implicit integer*2 (a-z) real*8 xp, r1, n1, r2, n2 integer*2 presx(mxpart,*), grptot(*) xp = 0.0d0 r1 = DFLOAT(prtot) n1 = DFLOAT(N) do 10 i=1, ngrp r2 = DFLOAT(presx(i, ix)) n2 = DFLOAT(grptot(i)) 20 if(r2.gt.(0.1)) then xp = xp+ DLOG(n2/n1) + DLOG(r1/r2) n1 = n1-1.0D0 n2 = n2-1.0D0 r1 = r1-1.0D0 r2 = r2-1.0D0 go to 20 endif 10 continue return end

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Appendix 4D Permutations used in Fisher-Pitman Test Example

FISHER-PITMAN TEST, JSF 1.2.95 SODIUM, MALES GROUP 1 VS GROUP 2 1 -1446.60 -1449.40 10 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 -1446.80 -1449.40 10 10 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 3 -1446.90 -1449.40 11 11 12 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 4 -1447.40 -1449.40 12 12 13 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 5 -1448.40 -1449.40 13 13 14 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 6 -1448.50 -1449.40 14 14 15 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 7 -1448.80 -1449.40 15 15 16 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 8 -1449.10 -1449.40 16 16 17 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 9 -1449.40 -1449.40 17 17 18 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 10 -1447.30 -1449.40 9 9 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 11 -1447.40 -1449.40 11 11 12 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 12 -1447.90 -1449.40 12 12 13 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 13 -1448.90 -1449.40 13 13 14 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 14 -1449.00 -1449.40 14 14 15 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 15 -1449.30 -1449.40 15 15 16 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 16 -1447.60 -1449.40 10 10 12 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 17 -1448.10 -1449.40 12 12 13 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 18 -1449.10 -1449.40 13 13 14 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 19 -1449.20 -1449.40 14 14 15 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 20 -1448.20 -1449.40 11 11 13 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 21 -1449.20 -1449.40 13 13 14 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 22 -1449.30 -1449.40 14 14 15 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 23 -1448.00 -1449.40 8 8 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 24 -1448.10 -1449.40 11 11 12 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 25 -1448.60 -1449.40 12 12 13 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 26 -1448.30 -1449.40 10 10 12 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 27 -1448.80 -1449.40 12 12 13 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 28 -1448.90 -1449.40 11 11 13 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 29 -1448.80 -1449.40 9 9 12 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 30 -1449.30 -1449.40 12 12 13 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 31 -1449.40 -1449.40 11 11 13 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 32 -1448.30 -1449.40 7 7 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 33 -1448.40 -1449.40 11 11 12 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 34 -1448.90 -1449.40 12 12 13 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 35 -1448.60 -1449.40 10 10 12 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 36 -1449.10 -1449.40 12 12 13 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 37 -1449.20 -1449.40 11 11 13 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 38 -1449.10 -1449.40 9 9 12 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 39 -1449.00 -1449.40 6 6 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 40 -1449.10 -1449.40 11 11 12 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 41 -1449.30 -1449.40 10 10 12 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 42 -1449.40 -1449.40 5 5 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 GROUP 1 VS GROUP 3 1 -1452.80 -1454.90 10 1 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 -1452.90 -1454.90 10 10 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 3 -1453.30 -1454.90 11 11 12 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 4 -1454.30 -1454.90 12 12 13 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 5 -1454.40 -1454.90 13 13 14 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 6 -1454.70 -1454.90 14 14 15 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 7 -1453.00 -1454.90 9 9 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 8 -1453.40 -1454.90 11 11 12 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 9 -1454.40 -1454.90 12 12 13 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 10 -1454.50 -1454.90 13 13 14 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 11 -1454.80 -1454.90 14 14 15 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 12 -1453.10 -1454.90 10 10 11 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 13 -1453.50 -1454.90 11 11 12 1 1 1 1 1 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 14 -1454.50 -1454.90 12 12 13 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 15 -1454.60 -1454.90 13 13 14 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 16 -1454.90 -1454.90 14 14 15 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 17 -1454.90 -1454.90 11 11 13 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 18 -1453.20 -1454.90 8 8 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 19 -1453.60 -1454.90 11 11 12 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 20 -1454.60 -1454.90 12 12 13 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 21 -1454.70 -1454.90 13 13 14 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0

ROELEE 3.1 166

22 -1453.30 -1454.90 10 10 11 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 23 -1453.70 -1454.90 11 11 12 1 1 1 1 1 1 1 0 1 0 2 0 0 0 0 0 0 0 0 0 24 -1454.70 -1454.90 12 12 13 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 25 -1454.80 -1454.90 13 13 14 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 26 -1453.40 -1454.90 9 9 11 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 27 -1453.80 -1454.90 11 11 12 1 1 1 1 1 1 1 0 0 1 2 0 0 0 0 0 0 0 0 0 28 -1454.80 -1454.90 12 12 13 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 29 -1454.90 -1454.90 13 13 14 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 30 -1453.90 -1454.90 10 10 12 1 1 1 1 1 1 1 0 0 1 2 0 0 0 0 0 0 0 0 0 31 -1454.90 -1454.90 12 12 13 1 1 1 1 1 1 1 0 0 0 2 1 0 0 0 0 0 0 0 0 32 -1453.40 -1454.90 7 7 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 33 -1453.80 -1454.90 11 11 12 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 34 -1454.80 -1454.90 12 12 13 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 35 -1454.90 -1454.90 13 13 14 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 36 -1453.50 -1454.90 10 10 11 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 37 -1453.90 -1454.90 11 11 12 1 1 1 1 1 1 0 1 1 0 2 0 0 0 0 0 0 0 0 0 38 -1454.90 -1454.90 12 12 13 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 39 -1453.60 -1454.90 9 9 11 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 40 -1454.00 -1454.90 11 11 12 1 1 1 1 1 1 0 1 0 1 2 0 0 0 0 0 0 0 0 0 41 -1454.10 -1454.90 10 10 12 1 1 1 1 1 1 0 1 0 1 2 0 0 0 0 0 0 0 0 0 42 -1453.80 -1454.90 8 8 11 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 43 -1454.20 -1454.90 11 11 12 1 1 1 1 1 1 0 0 1 1 2 0 0 0 0 0 0 0 0 0 44 -1454.30 -1454.90 10 10 12 1 1 1 1 1 1 0 0 1 1 2 0 0 0 0 0 0 0 0 0 45 -1454.40 -1454.90 9 9 12 1 1 1 1 1 1 0 0 1 1 2 0 0 0 0 0 0 0 0 0 46 -1454.60 -1454.90 6 6 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 47 -1454.70 -1454.90 10 10 11 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 48 -1454.80 -1454.90 9 9 11 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 GROUP 1 VS GROUP 4 1 -1428.70 -1428.70 9 1 11 1 1 1 1 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0

ROELEE 3.1 167

Appendix 4E Extra Dunnett Tables

Dunnett's test, two sided, alpha = 0.005

Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.000 3 7.454 8.872 4 5.598 6.491 7.016 5 4.773 5.446 5.841 6.118 6.332 6.504 6.649 6.773 6.882 6.978 7.065 7.144 7.216 7.282 7.343 7.401 7.454 7.504 7.551 7.596 6 4.317 4.872 5.197 5.425 5.600 5.742 5.862 5.964 6.054 6.133 6.205 6.270 6.329 6.384 6.435 6.482 6.526 6.568 6.607 6.644 7 4.029 4.513 4.795 4.992 5.144 5.268 5.371 5.460 5.537 5.607 5.669 5.725 5.777 5.824 5.869 5.910 5.948 5.984 6.018 6.050 8 3.833 4.268 4.521 4.699 4.835 4.945 5.038 5.117 5.187 5.249 5.305 5.355 5.402 5.444 5.484 5.521 5.555 5.588 5.618 5.647 9 3.690 4.091 4.324 4.486 4.612 4.713 4.798 4.871 4.935 4.991 5.043 5.089 5.131 5.171 5.207 5.241 5.272 5.302 5.330 5.357 10 3.581 3.958 4.175 4.327 4.443 4.538 4.617 4.685 4.744 4.797 4.845 4.888 4.928 4.964 4.998 5.030 5.059 5.087 5.113 5.138 11 3.497 3.853 4.058 4.202 4.312 4.401 4.476 4.540 4.596 4.646 4.691 4.732 4.769 4.804 4.835 4.865 4.893 4.919 4.944 4.967 12 3.428 3.769 3.965 4.102 4.207 4.292 4.363 4.424 4.477 4.525 4.568 4.606 4.642 4.675 4.705 4.733 4.760 4.785 4.808 4.830 13 3.372 3.701 3.889 4.020 4.121 4.202 4.270 4.329 4.380 4.426 4.467 4.504 4.538 4.570 4.599 4.626 4.651 4.675 4.697 4.719 14 3.326 3.643 3.825 3.952 4.049 4.128 4.193 4.250 4.299 4.343 4.383 4.419 4.452 4.482 4.510 4.536 4.561 4.584 4.605 4.626 15 3.286 3.595 3.771 3.894 3.988 4.064 4.128 4.183 4.231 4.273 4.312 4.347 4.378 4.408 4.435 4.460 4.484 4.506 4.527 4.547 16 3.252 3.553 3.725 3.845 3.936 4.010 4.072 4.126 4.172 4.214 4.251 4.285 4.316 4.344 4.371 4.395 4.418 4.440 4.460 4.480 17 3.222 3.517 3.685 3.802 3.891 3.964 4.024 4.076 4.122 4.162 4.198 4.231 4.262 4.289 4.315 4.339 4.362 4.383 4.403 4.421 18 3.197 3.486 3.650 3.765 3.852 3.923 3.982 4.033 4.077 4.117 4.152 4.185 4.214 4.241 4.266 4.290 4.312 4.333 4.352 4.370 19 3.174 3.458 3.619 3.732 3.817 3.887 3.945 3.995 4.038 4.077 4.112 4.143 4.172 4.199 4.224 4.247 4.268 4.288 4.307 4.325 20 3.153 3.433 3.592 3.702 3.787 3.855 3.912 3.961 4.004 4.042 4.076 4.107 4.135 4.161 4.186 4.208 4.229 4.249 4.268 4.286 35 2.996 3.242 3.381 3.476 3.550 3.608 3.658 3.700 3.737 3.770 3.799 3.826 3.850 3.873 3.893 3.913 3.931 3.948 3.964 3.979 120 2.861 3.078 3.200 3.284 3.347 3.398 3.441 3.478 3.510 3.538 3.563 3.586 3.607 3.627 3.644 3.661 3.677 3.691 3.705 3.718 32000 2.807 3.014 3.130 3.209 3.269 3.317 3.357 3.392 3.422 3.448 3.472 3.494 3.513 3.532 3.548 3.564 3.579 3.592 3.605 3.618 -1 2.807 3.014 3.129 3.209 3.269 3.317 3.357 3.391 3.421 3.448 3.472 3.493 3.513 3.531 3.548 3.564 3.578 3.592 3.605 3.617

Dunnett's test, two sided, alpha = 0.002 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.000 310.00010.000 4 7.174 8.286 8.942 5 5.894 6.690 7.158 7.489 7.743 7.950 8.123 8.271 8.401 8.517 8.621 8.715 8.802 8.881 8.955 9.023 9.087 9.147 9.204 9.258 6 5.208 5.842 6.214 6.477 6.680 6.844 6.981 7.100 7.204 7.296 7.379 7.455 7.524 7.587 7.646 7.701 7.753 7.801 7.846 7.889 7 4.785 5.324 5.639 5.861 6.032 6.171 6.287 6.388 6.476 6.554 6.624 6.688 6.747 6.801 6.851 6.897 6.941 6.982 7.021 7.057 8 4.501 4.976 5.254 5.449 5.600 5.722 5.824 5.913 5.990 6.059 6.121 6.177 6.229 6.276 6.320 6.361 6.400 6.436 6.470 6.502 9 4.297 4.728 4.979 5.156 5.292 5.402 5.495 5.575 5.645 5.707 5.763 5.814 5.860 5.903 5.943 5.980 6.015 6.048 6.079 6.108 10 4.144 4.543 4.774 4.937 5.062 5.164 5.249 5.323 5.387 5.444 5.496 5.543 5.586 5.625 5.662 5.696 5.728 5.759 5.787 5.814 11 4.025 4.399 4.615 4.768 4.885 4.980 5.059 5.128 5.188 5.242 5.290 5.334 5.374 5.411 5.445 5.477 5.507 5.535 5.562 5.587 12 3.930 4.284 4.489 4.633 4.744 4.833 4.908 4.973 5.030 5.080 5.126 5.167 5.205 5.240 5.272 5.303 5.331 5.357 5.382 5.406 13 3.852 4.191 4.386 4.523 4.629 4.714 4.786 4.847 4.901 4.949 4.993 5.032 5.068 5.101 5.132 5.161 5.188 5.213 5.237 5.259 14 3.787 4.113 4.301 4.432 4.533 4.615 4.684 4.743 4.795 4.841 4.882 4.920 4.954 4.986 5.016 5.043 5.069 5.093 5.116 5.138 15 3.733 4.048 4.229 4.356 4.453 4.532 4.598 4.655 4.705 4.749 4.789 4.826 4.859 4.889 4.918 4.944 4.969 4.992 5.014 5.035 16 3.686 3.992 4.167 4.290 4.384 4.461 4.525 4.580 4.628 4.671 4.710 4.745 4.777 4.807 4.834 4.860 4.884 4.907 4.928 4.948 17 3.646 3.943 4.114 4.234 4.325 4.399 4.462 4.515 4.562 4.604 4.641 4.676 4.707 4.736 4.762 4.787 4.811 4.832 4.853 4.873 18 3.611 3.901 4.068 4.184 4.274 4.346 4.407 4.459 4.505 4.545 4.582 4.615 4.645 4.673 4.700 4.724 4.746 4.768 4.788 4.807 19 3.579 3.864 4.027 4.141 4.228 4.299 4.358 4.409 4.454 4.494 4.529 4.562 4.591 4.619 4.644 4.668 4.690 4.711 4.731 4.749 20 3.552 3.831 3.991 4.103 4.188 4.257 4.315 4.365 4.409 4.448 4.483 4.515 4.544 4.571 4.595 4.619 4.640 4.661 4.680 4.698 35 3.340 3.579 3.715 3.809 3.882 3.940 3.989 4.031 4.067 4.100 4.129 4.156 4.180 4.203 4.223 4.243 4.261 4.278 4.294 4.309 120 3.161 3.368 3.484 3.564 3.625 3.674 3.715 3.751 3.782 3.809 3.834 3.856 3.876 3.895 3.912 3.929 3.944 3.958 3.972 3.984 32000 3.091 3.285 3.394 3.469 3.526 3.572 3.610 3.643 3.672 3.697 3.720 3.741 3.760 3.777 3.793 3.808 3.822 3.835 3.848 3.860 -1 3.090 3.285 3.393 3.468 3.525 3.571 3.610 3.642 3.671 3.697 3.719 3.740 3.759 3.777 3.793 3.808 3.822 3.835 3.847 3.859

ROELEE 3.1 168

Dunnett's test, two sided, alpha = 0.001 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.000 310.00010.000 4 8.612 9.92810.000 5 6.870 7.776 8.311 8.690 8.981 9.217 9.415 9.586 9.735 9.868 9.98710.00010.00010.00010.00010.00010.00010.00010.00010.000 6 5.959 6.663 7.078 7.371 7.597 7.780 7.934 8.067 8.183 8.286 8.379 8.464 8.541 8.612 8.678 8.740 8.797 8.851 8.902 8.950 7 5.408 5.994 6.338 6.581 6.769 6.921 7.049 7.159 7.256 7.342 7.420 7.490 7.554 7.614 7.669 7.720 7.768 7.813 7.856 7.896 8 5.042 5.551 5.850 6.061 6.224 6.356 6.467 6.562 6.646 6.721 6.788 6.849 6.905 6.957 7.005 7.049 7.091 7.130 7.168 7.203 9 4.781 5.238 5.505 5.694 5.839 5.957 6.056 6.142 6.217 6.284 6.344 6.398 6.448 6.495 6.538 6.577 6.615 6.650 6.683 6.714 10 4.587 5.006 5.250 5.422 5.555 5.662 5.753 5.831 5.899 5.960 6.015 6.065 6.111 6.153 6.192 6.228 6.263 6.295 6.325 6.354 11 4.437 4.827 5.053 5.213 5.336 5.436 5.520 5.592 5.656 5.712 5.763 5.809 5.851 5.891 5.927 5.961 5.992 6.022 6.050 6.077 12 4.318 4.685 4.898 5.048 5.163 5.257 5.335 5.403 5.463 5.516 5.563 5.607 5.647 5.683 5.717 5.749 5.779 5.807 5.833 5.858 13 4.221 4.569 4.771 4.913 5.023 5.111 5.186 5.250 5.307 5.357 5.402 5.443 5.481 5.515 5.547 5.577 5.606 5.632 5.657 5.681 14 4.141 4.474 4.667 4.803 4.907 4.992 5.063 5.124 5.178 5.225 5.268 5.308 5.344 5.377 5.407 5.436 5.463 5.488 5.512 5.534 15 4.073 4.394 4.579 4.709 4.810 4.891 4.959 5.018 5.069 5.115 5.157 5.194 5.229 5.260 5.290 5.317 5.343 5.367 5.390 5.412 16 4.015 4.325 4.504 4.630 4.727 4.805 4.871 4.928 4.977 5.022 5.061 5.098 5.131 5.161 5.190 5.216 5.241 5.264 5.286 5.307 17 3.965 4.266 4.440 4.562 4.655 4.731 4.795 4.850 4.898 4.941 4.979 5.015 5.047 5.076 5.104 5.129 5.153 5.176 5.197 5.217 18 3.922 4.215 4.384 4.502 4.593 4.667 4.729 4.782 4.829 4.871 4.908 4.942 4.973 5.002 5.029 5.054 5.077 5.099 5.120 5.139 19 3.884 4.170 4.335 4.450 4.539 4.611 4.671 4.723 4.769 4.809 4.846 4.879 4.909 4.937 4.963 4.988 5.010 5.032 5.052 5.071 20 3.850 4.130 4.291 4.404 4.491 4.561 4.620 4.671 4.715 4.755 4.790 4.823 4.852 4.880 4.905 4.929 4.951 4.972 4.992 5.010 35 3.591 3.827 3.961 4.054 4.126 4.184 4.232 4.274 4.311 4.343 4.372 4.399 4.423 4.446 4.467 4.486 4.504 4.521 4.537 4.553 120 3.376 3.575 3.688 3.766 3.825 3.873 3.913 3.948 3.978 4.005 4.029 4.051 4.071 4.089 4.106 4.122 4.137 4.151 4.164 4.177 32000 3.291 3.477 3.581 3.654 3.709 3.753 3.790 3.822 3.850 3.874 3.896 3.916 3.935 3.952 3.967 3.982 3.996 4.009 4.021 4.032 -1 3.291 3.477 3.581 3.653 3.708 3.752 3.789 3.821 3.849 3.874 3.896 3.916 3.934 3.951 3.967 3.982 3.995 4.008 4.020 4.032

ROELEE 3.1 169

Appendix 4F Command File TLEVENE.CMD

+ *** + *** Command File TLEVENE.CMD + *** Used to test DATATOX F1 Statistics + *** Levene Test - Form correct variable and send + *** in through Kruskal Wallis test + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SELECT SET SEX 0 SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 0 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 SET FACTOR GROUP .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 4G - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C: $36 5 :C: $36 6 :CO $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation $36 $36 further heading for group comparison analyses $36 11:L: $36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm $36 14TB: T T T T

ROELEE 3.1 170

$36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 1 1 1 $18 .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 1 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 FOR GROUP 1 CALC A1 = 150.02 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 2 CALC A1 = 144.94 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 3 CALC A1 = 145.49 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 4 CALC A1 = 142.87 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM

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NAME R3 "ABS(Sodium - group mean)" FOR SEX 1 .SET HEAD $136 6 :COMales INDEX .SET LIST $31 List Fields options $31 $31 1) Include heading ? Y $31 2) Change character codes to numeric equivalents ? N $31 LIST F1-F3,SODIUM,R3 &KWALLIS R3 + *** Females FOR GROUP 1 CALC A1 = 145.6444 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 2 CALC A1 = 141.48 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 3 CALC A1 = 144.69 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 4 CALC A1 = 147.44 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR SEX 2 .SET HEAD $136 6 :COFemales INDEX LIST F1-F3,SODIUM,R3 &KWALLIS R3 + + *** MALES and Females FOR GROUP 1 CALC A1 = 147.947368 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 2 CALC A1 = 143.21 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 3 CALC A1 = 145.09 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1) CALC R3 = A1 - SODIUM FOR GROUP 4 CALC A1 = 145.155 *FOR (SODIUM >A1) CALC R3 = SODIUM -A1 *FOR (SODIUM <A1)

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CALC R3 = A1 - SODIUM .SET HEAD $136 6 :COMales and Females FOR INDEX LIST F1-F3,SODIUM,R3 &KWALLIS R3 WRITE ITLEVENE

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Appendix 4G

Results from TLEVENE.CMD Appendix 4G - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Males + *** table generated : 24-FEB-95, 15:08:10 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 0 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 1 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Male Factor of interest: F3 Group FIELDS: (Cut-points if >0) F1 Animal Reference F2(1) Sex F3(1) Group F79(146) Sodium at 6 months (mmol/l) F158 ABS(Sodium - group mean) List Fields options 1) Include heading ? Y 2) Change character codes to numeric equivalents ? N

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Appendix 4G - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Males #1 1001 |m |a |150.0 |0.020000| #2 1002 |m |a |148.1 |1.920000| #3 1003 |m |a |150.3 |0.280000| #4 1004 |m |a |149.9 |0.120000| #5 1005 |m |a |150.6 |0.580000| #6 1006 |m |a |153.2 |3.180000| #7 1007 |m |a |148.3 |1.720000| #8 1008 |m |a |152.5 |2.480000| #9 1009 |m |a |148.9 |1.120000| #10 1010 |m |a |148.4 |1.620000| #21 2001 |m |b |145.9 |0.960000| #22 2002 |m |b |147.6 |2.660000| #23 2003 |m |b |150.9 |5.960000| #24 2004 |m |b |145.5 |0.560000| #25 2005 |m |b |146.9 |1.960000| #26 2006 |m |b |146.6 |1.660000| #27 2007 |m |b |143.8 |1.140000| #28 2008 |m |b |144.1 |0.840000| #29 2009 |m |b |140.6 |4.340000| #30 2010 |m |b |137.5 |7.440000| #41 3001 |m |c |138.0 |7.490000| #42 3002 |m |c |139.8 |5.690000| #43 3003 |m |c |147.9 |2.410000| #44 3004 |m |c |146.7 |1.210000| #45 3005 |m |c |145.8 |0.310000| #46 3006 |m |c |145.3 |0.190000| #47 3007 |m |c |144.5 |0.990000| #48 3008 |m |c |149.9 |4.410000| #49 3009 |m |c |148.5 |3.010000| #50 3010 |m |c |148.5 |3.010000| #61 4001 |m |d |141.8 |1.070000| #62 4002 |m |d |143.8 |0.930000| #63 4003 |m |d |145.4 |2.530000| #64 4004 |m |d |135.7 |7.170000| #65 4005 |m |d |145.1 |2.230000| #66 4006 |m |d |143.6 |0.730000| #67 4007 |m |d |144.4 |1.530000| #68 4008 |m |d |142.4 |0.470000| #69 4009 |m |d |143.6 |0.730000| #70 4010 |m |d |142.9 |0.030000| Kruskal-Wallis Analysis ABS(Sodium - group mean) Control 1 ppm 5 ppm 25 ppm Total Trend N 10 10 10 10 40 MRank 16.400000 23.900000 24.500000 17.200000 20.500000 Median 1.370000 1.810000 2.710000 1.000000 1.575000 Min 0.020000 0.560000 0.190000 0.030000 0.020000 Max 3.180000 7.440000 7.490000 7.170000 7.490000 Miss 0 0 0 0 0 Q1 0.020000 0.560000 0.190000 0.030000 0.020000 Q5 0.020000 0.560000 0.190000 0.030000 0.075000 Q25 0.280000 0.960000 0.990000 0.730000 0.730000 Q75 1.920000 4.340000 4.410000 2.230000 2.835000 Q95 3.180000 7.440000 7.490000 7.170000 7.305000 Q99 3.180000 7.440000 7.490000 7.170000 7.490000 QRange 1.640000 3.380000 3.420000 1.500000 2.105000 ChiSq 2.062857 2.287434 0.022874 4.044173 0.622324 P 0.150927 0.130425 0.879784 0.256734 0.430185 Stl P 0.344508 0.303286 0.997638 ExP 0.165494 0.137782 1.000000

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Appendix 4G - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Females + *** table generated : 24-FEB-95, 15:08:25 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 0 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 2 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Female Factor of interest: F3 Group FIELDS: (Cut-points if >0) F1 Animal Reference F2(1) Sex F3(1) Group F79(146) Sodium at 6 months (mmol/l) F158 ABS(Sodium - group mean) List Fields options 1) Include heading ? Y 2) Change character codes to numeric equivalents ? N

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Appendix 4G - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Females #11 1011 |f |a |145.3 |0.344400| #12 1012 |f |a |147.4 |1.755600| #13 1013 |f |a |145.1 |0.544400| #14 1014 |f |a |* |* | #15 1015 |f |a |145.7 |0.055600| #16 1016 |f |a |144.5 |1.144400| #17 1017 |f |a |146.3 |0.655600| #18 1018 |f |a |147.2 |1.555600| #19 1019 |f |a |145.3 |0.344400| #20 1020 |f |a |144.0 |1.644400| #31 2011 |f |b |147.9 |6.420000| #32 2012 |f |b |145.4 |3.920000| #33 2013 |f |b |141.5 |0.020000| #34 2014 |f |b |141.8 |0.320000| #35 2015 |f |b |138.0 |3.480000| #36 2016 |f |b |142.9 |1.420000| #37 2017 |f |b |127.4 |14.08000| #38 2018 |f |b |140.9 |0.580000| #39 2019 |f |b |142.6 |1.120000| #40 2020 |f |b |146.4 |4.920000| #51 3011 |f |c |134.4 |10.29000| #52 3012 |f |c |132.1 |12.59000| #53 3013 |f |c |142.2 |2.490000| #54 3014 |f |c |148.9 |4.210000| #55 3015 |f |c |147.1 |2.410000| #56 3016 |f |c |149.5 |4.810000| #57 3017 |f |c |150.2 |5.510000| #58 3018 |f |c |146.3 |1.610000| #59 3019 |f |c |148.1 |3.410000| #60 3020 |f |c |148.1 |3.410000| #71 4011 |f |d |149.3 |1.860000| #72 4012 |f |d |148.5 |1.060000| #73 4013 |f |d |147.4 |0.040000| #74 4014 |f |d |149.4 |1.960000| #75 4015 |f |d |144.4 |3.040000| #76 4016 |f |d |149.7 |2.260000| #77 4017 |f |d |148.3 |0.860000| #78 4018 |f |d |145.8 |1.640000| #79 4019 |f |d |145.6 |1.840000| #80 4020 |f |d |146.0 |1.440000| Kruskal-Wallis Analysis ABS(Sodium - group mean) Control 1 ppm 5 ppm 25 ppm Total Trend N 9 10 10 10 39 MRank 10.888889 20.900000 30.000000 17.300000 20.000000 Median 0.655600 2.450000 3.810000 1.740000 1.755600 Min 0.055600 0.020000 1.610000 0.040000 0.020000 Max 1.755600 14.080000 12.590000 3.040000 14.080000 Miss 1 0 0 0 1 Q1 0.055600 0.020000 1.610000 0.040000 0.020000 Q5 0.055600 0.020000 1.610000 0.040000 0.040000 Q25 0.344400 0.580000 2.490000 1.060000 0.860000 Q75 1.555600 4.920000 5.510000 1.960000 3.480000 Q95 1.755600 14.080000 12.590000 3.040000 12.590000 Q99 1.755600 14.080000 12.590000 3.040000 14.080000 QRange 1.211200 4.340000 3.020000 0.900000 2.620000 ChiSq 1.708165 12.348330 3.529763 14.065240 0.052402 P 0.191224 0.000441 0.060276 0.002818 0.818936 Stl P 0.416602 0.001285 0.149116 ExP 1.000000 0.000087 0.062374

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Appendix 4G - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Males and Females + *** table generated : 24-FEB-95, 15:08:32 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 0 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F1 Animal Reference F2(1) Sex F3(1) Group F79(146) Sodium at 6 months (mmol/l) F158 ABS(Sodium - group mean) List Fields options 1) Include heading ? Y 2) Change character codes to numeric equivalents ? N

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Appendix 4G - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Males and Females #1 1001 |m |a |150.0 |2.052632| #2 1002 |m |a |148.1 |0.152632| #3 1003 |m |a |150.3 |2.352632| #4 1004 |m |a |149.9 |1.952632| #5 1005 |m |a |150.6 |2.652632| #6 1006 |m |a |153.2 |5.252632| #7 1007 |m |a |148.3 |0.352632| #8 1008 |m |a |152.5 |4.552632| #9 1009 |m |a |148.9 |0.952632| #10 1010 |m |a |148.4 |0.452632| #11 1011 |f |a |145.3 |2.647368| #12 1012 |f |a |147.4 |0.547368| #13 1013 |f |a |145.1 |2.847368| #14 1014 |f |a |* |* | #15 1015 |f |a |145.7 |2.247368| #16 1016 |f |a |144.5 |3.447368| #17 1017 |f |a |146.3 |1.647368| #18 1018 |f |a |147.2 |0.747368| #19 1019 |f |a |145.3 |2.647368| #20 1020 |f |a |144.0 |3.947368| #21 2001 |m |b |145.9 |2.690000| #22 2002 |m |b |147.6 |4.390000| #23 2003 |m |b |150.9 |7.690000| #24 2004 |m |b |145.5 |2.290000| #25 2005 |m |b |146.9 |3.690000| #26 2006 |m |b |146.6 |3.390000| #27 2007 |m |b |143.8 |0.590000| #28 2008 |m |b |144.1 |0.890000| #29 2009 |m |b |140.6 |2.610000| #30 2010 |m |b |137.5 |5.710000| #31 2011 |f |b |147.9 |4.690000| #32 2012 |f |b |145.4 |2.190000| #33 2013 |f |b |141.5 |1.710000| #34 2014 |f |b |141.8 |1.410000| #35 2015 |f |b |138.0 |5.210000| #36 2016 |f |b |142.9 |0.310000| #37 2017 |f |b |127.4 |15.81000| #38 2018 |f |b |140.9 |2.310000| #39 2019 |f |b |142.6 |0.610000| #40 2020 |f |b |146.4 |3.190000| #41 3001 |m |c |138.0 |7.090000| #42 3002 |m |c |139.8 |5.290000| #43 3003 |m |c |147.9 |2.810000| #44 3004 |m |c |146.7 |1.610000| #45 3005 |m |c |145.8 |0.710000| #46 3006 |m |c |145.3 |0.210000| #47 3007 |m |c |144.5 |0.590000| #48 3008 |m |c |149.9 |4.810000| #49 3009 |m |c |148.5 |3.410000| #50 3010 |m |c |148.5 |3.410000| #51 3011 |f |c |134.4 |10.69000| #52 3012 |f |c |132.1 |12.99000| #53 3013 |f |c |142.2 |2.890000| #54 3014 |f |c |148.9 |3.810000| #55 3015 |f |c |147.1 |2.010000| #56 3016 |f |c |149.5 |4.410000| #57 3017 |f |c |150.2 |5.110000| #58 3018 |f |c |146.3 |1.210000| #59 3019 |f |c |148.1 |3.010000| #60 3020 |f |c |148.1 |3.010000| #61 4001 |m |d |141.8 |3.355000| #62 4002 |m |d |143.8 |1.355000|

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Appendix 4G - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Field List Males and Females #63 4003 |m |d |145.4 |0.245000| #64 4004 |m |d |135.7 |9.455000| #65 4005 |m |d |145.1 |0.055000| #66 4006 |m |d |143.6 |1.555000| #67 4007 |m |d |144.4 |0.755000| #68 4008 |m |d |142.4 |2.755000| #69 4009 |m |d |143.6 |1.555000| #70 4010 |m |d |142.9 |2.255000| #71 4011 |f |d |149.3 |4.145000| #72 4012 |f |d |148.5 |3.345000| #73 4013 |f |d |147.4 |2.245000| #74 4014 |f |d |149.4 |4.245000| #75 4015 |f |d |144.4 |0.755000| #76 4016 |f |d |149.7 |4.545000| #77 4017 |f |d |148.3 |3.145000| #78 4018 |f |d |145.8 |0.645000| #79 4019 |f |d |145.6 |0.445000| #80 4020 |f |d |146.0 |0.845000| Kruskal-Wallis Analysis ABS(Sodium - group mean) Control 1 ppm 5 ppm 25 ppm Total Trend N 19 20 20 20 79 MRank 33.789474 43.725000 48.275000 33.900000 40.000000 Median 2.247368 2.650000 3.210000 1.900000 2.647368 Min 0.152632 0.310000 0.210000 0.055000 0.055000 Max 5.252632 15.810000 12.990000 9.455000 15.810000 Miss 1 0 0 0 1 Q1 0.152632 0.310000 0.210000 0.055000 0.055000 Q5 0.152632 0.450000 0.400000 0.150000 0.245000 Q25 0.747368 1.560000 1.810000 0.755000 0.952632 Q75 2.847368 4.540000 4.960000 3.350000 3.947368 Q95 5.252632 11.750000 11.840000 7.000000 9.455000 Q99 5.252632 15.810000 12.990000 9.455000 15.810000 QRange 2.100000 2.980000 3.150000 2.595000 2.994736 ChiSq 1.744124 4.208383 0.003159 5.932206 1.074445 P 0.186617 0.040225 0.955180 0.114956 0.299944 Stl P 0.408118 0.102432 0.999873 ExP

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Appendix 5A Command File TKWALL.CMD

+ *** + *** Command File TKWALL.CMD + *** Used to test DATATOX F1 Statistics + *** Non-Parametric Statistics - + *** Median + *** Quantiles + *** Min, Max + *** Quartile Range + *** 2-way tests via KWALLIS (= WILCOXON) + *** Adjustments 1) Steel + *** 2-5) Various Bonferronni Tests + *** Total test via KWALLIS + *** Trend test via 1)Fry-Lee 2)Jonckeere + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SEX 1 SELECT SET SEX 0 +SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 SET FACTOR GROUP .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 5B - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C: $36 5 :C: $36 6 :CO $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36

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$36 further heading for individual animal reports $36 10:L:Animal Tissue Observation $36 $36 further heading for group comparison analyses $36 11:L: $36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm $36 14TB: T T T T $36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 1 1 1 $18 + + *** Start with MALES FOR SEX 1 .SET HEAD $136 6 :COMales .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 1 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 KWALLIS SODIUM .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? N $13 2) Mean Ranks ? N $13 3) Median Values ? N $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? N $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? N $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y

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$13 12) Quantiles ? N $13 13) Quantile range ? N $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $13 16) Missing Values ? N $13 + + JONCKEERE rather than Roelee SET CONT 0 &KWALLIS + Finally run through different Bonferonni adjustments SET CONT 1 .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET KWALL $113 6) Kruskal-Wallis statistic ? n $113 7) Print probabilities ? N $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 2 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 3 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 4 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 5 &KWALL .SET KWALL $113 6) Kruskal-Wallis statistic ? Y $113 7) Print probabilities ? Y $113 14) Trend Test 1)RoeLee 2)Jonckeere 1 $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &KWALL /LUD .SET KWALL $113 6) Kruskal-Wallis statistic ? Y $113 7) Print probabilities ? Y $113 14) Trend Test 1)RoeLee 2)Jonckeere 2 $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &KWALL /LUD =4 + + *** TO CHECK LUDIN, RE-DO KWALL TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &KWALL .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &KWALL + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + + *** REPEAT FOR FEMALES FOR SEX 2 .SET HEAD $136 6 :COFemales .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y

ROELEE 3.1 183

$13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 1 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 KWALLIS SODIUM .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? N $13 2) Mean Ranks ? N $13 3) Median Values ? N $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? N $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? N $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? N $13 13) Quantile range ? N $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $13 16) Missing Values ? N $13 + + JONCKEERE rather than Roelee SET CONT 0 &KWALLIS + Finally run through different Bonferonni adjustments SET CONT 1 .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET KWALL $113 6) Kruskal-Wallis statistic ? n $113 7) Print probabilities ? N $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 2 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 3 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 4 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 5 &KWALL .SET KWALL $113 6) Kruskal-Wallis statistic ? Y $113 7) Print probabilities ? Y $113 14) Trend Test 1)RoeLee 2)Jonckeere 1 $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &KWALL /LUD .SET KWALL $113 6) Kruskal-Wallis statistic ? Y $113 7) Print probabilities ? Y $113 14) Trend Test 1)RoeLee 2)Jonckeere 2 $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &KWALL /LUD =4 + + *** TO CHECK LUDIN, RE-DO KWALL TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High

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$18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &KWALL .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &KWALL + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + + *** REPEAT FOR MALES + FEMALES FOR .SET HEAD $136 6 :COMales and Females .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 1 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 KWALLIS SODIUM .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? N $13 2) Mean Ranks ? N $13 3) Median Values ? N $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? N $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? N $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? N $13 13) Quantile range ? N $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $13 16) Missing Values ? N $13 + + JONCKEERE rather than Roelee SET CONT 0 &KWALLIS + Finally run through different Bonferonni adjustments SET CONT 1 .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1

ROELEE 3.1 185

.SET KWALL $113 6) Kruskal-Wallis statistic ? n $113 7) Print probabilities ? N $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 2 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 3 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 4 &KWALL .SET KWALL $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 5 &KWALL .SET KWALL $113 6) Kruskal-Wallis statistic ? Y $113 7) Print probabilities ? Y $113 14) Trend Test 1)RoeLee 2)Jonckeere 1 $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &KWALL /LUD .SET KWALL $113 6) Kruskal-Wallis statistic ? Y $113 7) Print probabilities ? Y $113 14) Trend Test 1)RoeLee 2)Jonckeere 2 $113 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &KWALL /LUD =4 + + *** TO CHECK LUDIN, RE-DO KWALL TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &KWALL .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &KWALL + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: WRITE ITKWALL __________________________________________________________________

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Appendix 5B

Results from TKWALL.CMD Appendix 5B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males + *** table generated : 24-FEB-95, 15:04:44 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 1 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 1 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Male Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 5B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males Kruskal-Wallis/Fry-Lee options 1) Number of animals ? Y 2) Mean Ranks ? Y 3) Median Values ? Y 4) Confidence levels for Medians (give prob level): 0 5) Range (Minimum,Maximum) ? Y 6) Kruskal-Wallis statistic ? Y 7) Print probabilities ? Y 8) Print exact probabilities for comparisons ? Y 9) Yates correction ? Y 10) Minimum total outside one rank: 0 11) Show totals over partitions ? Y 12) Quantiles ? Y 13) Quartile range ? Y 14) Trend Test 1)RoeLee 2)Jonckheere 1 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 16) Missing Values ? Y

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1 Appendix 5B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 N 10 10 10 10 40 months (mmol/ MRank 33.650000 18.050000 20.250000 10.050000 20.500000 l) Median 149.950000 145.700000 146.250000 143.600000 145.850000 Min 148.100000 137.500000 138.000000 135.700000 135.700000 Max 153.200000 150.900000 149.900000 145.400000 153.200000 Miss 0 0 0 0 0 Q1 148.100000 137.500000 138.000000 135.700000 135.700000 Q5 148.100000 137.500000 138.000000 135.700000 137.750000 Q25 148.400000 143.800000 144.500000 142.400000 143.700000 Q75 150.600000 146.900000 148.500000 144.400000 148.500000 Q95 153.200000 150.900000 149.900000 145.400000 151.700000 Q99 153.200000 150.900000 149.900000 145.400000 153.200000 QRange 2.200000 3.100000 4.000000 2.000000 4.800000 ChiSq 10.080000 8.929142 14.296464 21.094989 12.509809 P 0.001499 0.002807 0.000156 0.000101 0.000405 Stl P 0.004317 0.007992 0.000461 ExP 0.000725 0.001624 0.000011 Jonckheere S = -356 ChiSq 21.094989 22.461801 P 0.000101 0.000007 KB1 P 0.010000 0.010000 0.000468 KB2 P 0.010000 0.010000 0.001000 KB3 P 0.010000 0.010000 0.001000 KB4 P 0.010000 0.010000 0.001000 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 ChiSq 12.509809 ChiSq 3.970084 ChiSq 10.080000 ChiSq P 0.000405 P 0.046315 P 0.001499 P Ludin procedure with alpha set at 0.001000 Jonckheere S = -356, -147 ChiSq 22.461801 ChiSq 8.617852 ChiSq 10.080000 8.929142 13.082595 P 0.000007 P 0.004642 P 0.000725 0.001624 0.001443 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = -147 ChiSq 10.080000 8.929142 13.082595 8.617852 P 0.001499 0.002807 0.001443 0.004642

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2 Appendix 5B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males Sodium at 6 months (mmol/l) Groups 3 and 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = -84 ChiSq 10.080000 10.080000 13.990587 P 0.001499 0.001499 0.000725

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Appendix 5B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Females + *** table generated : 24-FEB-95, 15:05:45 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 3 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 2 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Female Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 5B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Females Kruskal-Wallis/Fry-Lee options 1) Number of animals ? Y 2) Mean Ranks ? Y 3) Median Values ? Y 4) Confidence levels for Medians (give prob level): 0 5) Range (Minimum,Maximum) ? Y 6) Kruskal-Wallis statistic ? Y 7) Print probabilities ? Y 8) Print exact probabilities for comparisons ? Y 9) Yates correction ? Y 10) Minimum total outside one rank: 0 11) Show totals over partitions ? Y 12) Quantiles ? Y 13) Quartile range ? Y 14) Trend Test 1)RoeLee 2)Jonckheere 1 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 16) Missing Values ? Y

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3 Appendix 5B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 N 9 10 10 10 39 months (mmol/ MRank 18.222222 11.200000 23.150000 27.250000 20.000000 l) Median 145.300000 142.200000 147.600000 147.850000 145.800000 Min 144.000000 127.400000 132.100000 144.400000 127.400000 Max 147.400000 147.900000 150.200000 149.700000 150.200000 Miss 1 0 0 0 1 Q1 144.000000 127.400000 132.100000 144.400000 127.400000 Q5 144.000000 127.400000 132.100000 144.400000 132.100000 Q25 145.100000 140.900000 142.200000 145.800000 142.900000 Q75 146.300000 145.400000 148.900000 149.300000 148.100000 Q95 147.400000 147.900000 150.200000 149.700000 149.700000 Q99 147.400000 147.900000 150.200000 149.700000 150.200000 QRange 1.200000 4.500000 6.700000 3.500000 5.200000 ChiSq 3.843371 1.218206 4.689895 10.986713 6.736850 P 0.049943 0.269713 0.030341 0.011798 0.009444 Stl P 0.125311 0.551486 0.078608 ExP 0.050553 1.000000 0.029293 Jonckheere S = 172 ChiSq 10.986713 4.778741 P 0.011798 0.031350 KB1 P 1.000000 1.000000 0.100000 KB2 P 0.100000 1.000000 0.100000 KB3 P 0.100000 1.000000 0.100000 KB4 P 0.100000 1.000000 0.100000 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 ChiSq 6.736850 ChiSq 1.977121 ChiSq 3.843371 1.218206 5.290461 P 0.009444 P 0.159694 P 0.050553 0.269713 0.070989 Ludin procedure with alpha set at 0.001000 ChiSq 4.778741 ChiSq 3.843371 1.218206 4.689895 10.986713 P 0.031350 P 0.050553 0.269713 0.029293 0.011798 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = 27 ChiSq 3.843371 1.218206 5.290461 0.267201 P 0.049943 0.269713 0.070989 0.607084

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4 Appendix 5B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Females Sodium at 6 months (mmol/l) Groups 3 and 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = -48 ChiSq 3.843371 3.843371 4.071091 P 0.049943 0.049943 0.053476

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Appendix 5B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males and Females + *** table generated : 24-FEB-95, 15:06:44 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 5 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Kruskal-Wallis/Fry-Lee options 1) Number of animals ? Y 2) Mean Ranks ? Y 3) Median Values ? Y 4) Confidence levels for Medians (give prob level): 0 5) Range (Minimum,Maximum) ? Y 6) Kruskal-Wallis statistic ? Y 7) Print probabilities ? Y 8) Print exact probabilities for comparisons ? Y 9) Yates correction ? Y 10) Minimum total outside one rank: 0 11) Show totals over partitions ? Y 12) Quantiles ? Y 13) Quartile range ? Y 14) Trend Test 1)RoeLee 2)Jonckheere 1 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 16) Missing Values ? Y

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5 Appendix 5B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 N 19 20 20 20 79 months (mmol/ MRank 53.815789 28.450000 42.325000 36.100000 40.000000 l) Median 148.100000 143.950000 146.900000 145.250000 145.800000 Min 144.000000 127.400000 132.100000 135.700000 127.400000 Max 153.200000 150.900000 150.200000 149.700000 153.200000 Miss 1 0 0 0 1 Q1 144.000000 127.400000 132.100000 135.700000 127.400000 Q5 144.000000 132.450000 133.250000 138.750000 135.700000 Q25 145.300000 141.200000 143.350000 143.600000 143.600000 Q75 150.000000 146.500000 148.500000 147.850000 148.300000 Q95 153.200000 149.400000 150.050000 149.550000 150.600000 Q99 153.200000 150.900000 150.200000 149.700000 153.200000 QRange 4.700000 5.300000 5.150000 4.250000 4.700000 ChiSq 10.808199 2.137549 6.905970 12.739165 0.884368 P 0.001011 0.143731 0.008591 0.005236 0.347008 Stl P 0.002911 0.326061 0.023548 ExP Jonckheere S = -360 ChiSq 12.739165 2.491403 P 0.005236 0.116137 KB1 P 0.010000 1.000000 0.050000 KB2 P 0.010000 1.000000 0.050000 KB3 P 0.010000 1.000000 0.050000 KB4 P 0.010000 1.000000 0.050000 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 ChiSq 0.884368 ChiSq 10.808199 2.137549 6.905970 12.739165 P 0.347008 P 0.001011 0.143731 0.008591 0.005236 Ludin procedure with alpha set at 0.001000 ChiSq 2.491403 ChiSq 10.808199 2.137549 6.905970 12.739165 P 0.116137 P 0.001011 0.143731 0.008591 0.005236 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = -204 ChiSq 10.808199 2.137549 10.876837 2.009632 P 0.001011 0.143731 0.004346 0.158739

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6 Appendix 5B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males and Females Sodium at 6 months (mmol/l) Groups 3 and 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = -234 ChiSq 10.808199 10.808199 12.728692 P 0.001011 0.001011 0.000696

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Appendix 5C Extra Steel Tables



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Steel test, two sided, alpha = 0.0005 Number of Comparison Groups 1 2 3 4 5 6 7 8 9 4 3.481 3.661 3.762 5 3.481 3.660 3.761 3.832 3.885 3.928 3.965 3.996 4.023 6 3.481 3.660 3.761 3.831 3.885 3.928 3.964 3.995 4.022 7 3.481 3.660 3.761 3.831 3.885 3.928 3.964 3.995 4.022 8 3.481 3.660 3.761 3.831 3.884 3.928 3.964 3.995 4.022 9 3.481 3.660 3.761 3.831 3.884 3.927 3.963 3.994 4.021 10 3.481 3.660 3.761 3.831 3.884 3.927 3.963 3.994 4.021 11 3.481 3.660 3.761 3.831 3.884 3.927 3.963 3.994 4.021 12 3.481 3.660 3.761 3.831 3.884 3.927 3.963 3.994 4.021 13 3.481 3.660 3.761 3.830 3.884 3.927 3.963 3.994 4.021 14 3.481 3.660 3.760 3.830 3.884 3.927 3.963 3.994 4.021 15 3.481 3.660 3.760 3.830 3.884 3.927 3.963 3.994 4.021 16 3.481 3.660 3.760 3.830 3.884 3.927 3.963 3.993 4.020 17 3.481 3.660 3.760 3.830 3.884 3.927 3.963 3.993 4.020 18 3.481 3.660 3.760 3.830 3.883 3.926 3.962 3.993 4.020 19 3.481 3.660 3.760 3.830 3.883 3.926 3.962 3.993 4.020 20 3.481 3.660 3.760 3.830 3.883 3.926 3.962 3.993 4.020 __________________________________________________________________

ROELEE 3.1 199

Appendix 5D Tests of Jonckheere for small numbers

k, mk = 3 10 1 1 Sval P Cum P Stud T Normal -21 0.007576 0.007576 0.008640 0.016337 -19 0.015152 0.022727 0.021187 0.027275 -17 0.022727 0.045455 0.041651 0.043740 -15 0.030303 0.075758 0.071094 0.067426 -13 0.037879 0.113636 0.109963 0.099986 -11 0.045455 0.159091 0.158119 0.142754 -9 0.053030 0.212121 0.214883 0.196435 -7 0.060606 0.272727 0.279115 0.260821 -5 0.068182 0.340909 0.349289 0.334613 -3 0.075758 0.416667 0.423588 0.415427 -1 0.083333 0.500000 0.500000 0.500000 k, mk = 3 2 2 2 Sval P Cum P Stud T Normal -12 0.011111 0.011111 0.009868 0.014427 -10 0.022222 0.033333 0.035212 0.036878 -8 0.055556 0.088889 0.087387 0.082149 -6 0.077778 0.166667 0.172124 0.160258 -4 0.122222 0.288889 0.288127 0.275574 -2 0.133333 0.422222 0.426646 0.421257 0 0.155556 0.577778 0.426646 0.421257 k, mk = 3 3 3 3 Sval P Cum P Stud T Normal -27 0.000595 0.000595 0.000620 0.001933 -25 0.001190 0.001786 0.001887 0.003830 -23 0.002976 0.004762 0.004776 0.007254 -21 0.005952 0.010714 0.010490 0.013134 -19 0.010119 0.020833 0.020589 0.022750 -17 0.016071 0.036905 0.036860 0.037720 -15 0.024405 0.061310 0.061115 0.059907 -13 0.033333 0.094643 0.094924 0.091211 -11 0.044048 0.138690 0.139345 0.133260 -9 0.055357 0.194048 0.194689 0.187031 -7 0.065476 0.259524 0.260364 0.252493 -5 0.074405 0.333929 0.334839 0.328361 -3 0.081548 0.415476 0.415729 0.412070 -1 0.084524 0.500000 0.500000 0.500000 k, mk = 3 4 4 4 Sval P Cum P Stud T Normal -48 0.000029 0.000029 0.000049 0.000291 -46 0.000058 0.000087 0.000122 0.000494 -44 0.000144 0.000231 0.000278 0.000824 -42 0.000289 0.000519 0.000584 0.001346 -40 0.000577 0.001097 0.001146 0.002155 -38 0.000952 0.002049 0.002117 0.003383 -36 0.001616 0.003665 0.003709 0.005207 -34 0.002482 0.006147 0.006199 0.007860 -32 0.003781 0.009928 0.009935 0.011635 -30 0.005368 0.015296 0.015332 0.016894 -28 0.007561 0.022857 0.022861 0.024066 -26 0.010101 0.032958 0.033035 0.033639 -24 0.013362 0.046320 0.046382 0.046146 -22 0.016912 0.063232 0.063415 0.062141 -20 0.021154 0.084387 0.084596 0.082165 -18 0.025541 0.109928 0.110297 0.106700 -16 0.030476 0.140404 0.140768 0.136127 -14 0.035180 0.175584 0.176100 0.170675 -12 0.040144 0.215729 0.216203 0.210376

ROELEE 3.1 200

-10 0.044502 0.260231 0.260790 0.255034 -8 0.048745 0.308975 0.309381 0.304204 -6 0.051919 0.360895 0.361309 0.357197 -4 0.054661 0.415556 0.415745 0.413100 -2 0.056046 0.471602 0.471739 0.470826 0 0.056797 0.528398 0.471739 0.470826 k, mk = 3 5 5 5 Sval P Cum P Stud T Normal -75 0.000001 0.000001 0.000004 0.000046 -73 0.000003 0.000004 0.000008 0.000071 -71 0.000007 0.000011 0.000017 0.000109 -69 0.000013 0.000024 0.000033 0.000164 -67 0.000026 0.000050 0.000063 0.000245 -65 0.000048 0.000098 0.000114 0.000361 -63 0.000082 0.000180 0.000198 0.000528 -61 0.000133 0.000313 0.000335 0.000763 -59 0.000213 0.000526 0.000549 0.001092 -57 0.000325 0.000851 0.000874 0.001547 -55 0.000485 0.001336 0.001356 0.002168 -53 0.000700 0.002036 0.002052 0.003007 -51 0.000992 0.003029 0.003037 0.004129 -49 0.001372 0.004400 0.004400 0.005611 -47 0.001861 0.006261 0.006249 0.007548 -45 0.002472 0.008733 0.008711 0.010052 -43 0.003231 0.011964 0.011932 0.013252 -41 0.004148 0.016112 0.016073 0.017297 -39 0.005245 0.021357 0.021314 0.022352 -37 0.006527 0.027883 0.027844 0.028600 -35 0.008011 0.035894 0.035862 0.036238 -33 0.009690 0.045584 0.045570 0.045469 -31 0.011570 0.057154 0.057163 0.056505 -29 0.013633 0.070788 0.070829 0.069549 -27 0.015869 0.086657 0.086735 0.084798 -25 0.018245 0.104902 0.105020 0.102426 -23 0.020732 0.125634 0.125792 0.122578 -21 0.023284 0.148917 0.149116 0.145361 -19 0.025860 0.174778 0.175009 0.170831 -17 0.028403 0.203180 0.203437 0.198990 -15 0.030861 0.234041 0.234309 0.229778 -13 0.033169 0.267210 0.267479 0.263065 -11 0.035280 0.302490 0.302743 0.298656 -9 0.037132 0.339622 0.339846 0.336288 -7 0.038681 0.378303 0.378484 0.375636 -5 0.039881 0.418184 0.418311 0.416323 -3 0.040700 0.458884 0.458950 0.457928 -1 0.041116 0.500000 0.500000 0.500000 k, mk = 4 2 2 2 2 Sval P Cum P Stud T Normal -24 0.000397 0.000397 0.000505 0.001658 -22 0.001190 0.001587 0.001848 0.003665 -20 0.003571 0.005159 0.005290 0.007631 -18 0.007143 0.012302 0.012653 0.014977 -16 0.013889 0.026190 0.026341 0.027725 -14 0.022222 0.048413 0.049077 0.048462 -12 0.034524 0.082937 0.083458 0.080074 -10 0.047222 0.130159 0.131422 0.125238 -8 0.062698 0.192857 0.193742 0.185709 -6 0.075397 0.268254 0.269673 0.261593 -4 0.088095 0.356349 0.356839 0.350836 -2 0.094444 0.450794 0.451417 0.449198 0 0.098413 0.549206 0.451417 0.449198 k, mk = 4 3 3 3 3 Sval P Cum P Stud T Normal -54 0.000003 0.000003 0.000007 0.000083 -52 0.000008 0.000011 0.000020 0.000145 -50 0.000024 0.000035 0.000050 0.000249 -48 0.000060 0.000095 0.000116 0.000419

ROELEE 3.1 201

-46 0.000127 0.000222 0.000252 0.000692 -44 0.000249 0.000471 0.000509 0.001122 -42 0.000457 0.000928 0.000971 0.001786 -40 0.000782 0.001710 0.001757 0.002789 -38 0.001277 0.002987 0.003033 0.004276 -36 0.001994 0.004981 0.005023 0.006435 -34 0.002987 0.007968 0.008006 0.009508 -32 0.004321 0.012289 0.012326 0.013795 -30 0.006055 0.018344 0.018383 0.019654 -28 0.008225 0.026569 0.026622 0.027504 -26 0.010874 0.037443 0.037523 0.037811 -24 0.014010 0.051453 0.051568 0.051073 -22 0.017603 0.069056 0.069224 0.067797 -20 0.021615 0.090671 0.090900 0.088465 -18 0.025963 0.116634 0.116921 0.113497 -16 0.030517 0.147151 0.147495 0.143211 -14 0.035143 0.182294 0.182681 0.177777 -12 0.039678 0.221972 0.222373 0.217185 -10 0.043920 0.265893 0.266285 0.261216 -8 0.047708 0.313601 0.313952 0.309429 -6 0.050866 0.364467 0.364741 0.361169 -4 0.053231 0.417698 0.417874 0.415585 -2 0.054700 0.472397 0.472460 0.471672 0 0.055206 0.527603 0.472460 0.471672

ROELEE 3.1 202

k, mk = 4 4 4 4 4 Sval P Cum P Stud T Normal -96 0.000000 0.000000 0.000000 0.000005 -94 0.000000 0.000000 0.000000 0.000007 -92 0.000000 0.000000 0.000001 0.000011 -90 0.000000 0.000001 0.000001 0.000016 -88 0.000001 0.000001 0.000002 0.000024 -86 0.000002 0.000003 0.000005 0.000036 -84 0.000003 0.000006 0.000009 0.000053 -82 0.000006 0.000012 0.000016 0.000078 -80 0.000011 0.000023 0.000027 0.000113 -78 0.000018 0.000041 0.000047 0.000162 -76 0.000030 0.000071 0.000078 0.000231 -74 0.000047 0.000118 0.000127 0.000327 -72 0.000073 0.000191 0.000202 0.000458 -70 0.000110 0.000301 0.000314 0.000637 -68 0.000163 0.000465 0.000479 0.000879 -66 0.000236 0.000701 0.000716 0.001203 -64 0.000335 0.001036 0.001051 0.001632 -62 0.000466 0.001501 0.001516 0.002198 -60 0.000638 0.002139 0.002153 0.002936 -58 0.000858 0.002998 0.003009 0.003890 -56 0.001138 0.004136 0.004144 0.005113 -54 0.001487 0.005623 0.005628 0.006667 -52 0.001917 0.007541 0.007542 0.008625 -50 0.002438 0.009979 0.009977 0.011070 -48 0.003063 0.013042 0.013037 0.014097 -46 0.003800 0.016842 0.016836 0.017812 -44 0.004661 0.021503 0.021497 0.022332 -42 0.005651 0.027153 0.027151 0.027784 -40 0.006779 0.033932 0.033935 0.034301 -38 0.008044 0.041976 0.041988 0.042026 -36 0.009449 0.051425 0.051449 0.051103 -34 0.010988 0.062412 0.062454 0.061674 -32 0.012655 0.075067 0.075126 0.073881 -30 0.014434 0.089501 0.089581 0.087853 -28 0.016312 0.105813 0.105915 0.103707 -26 0.018264 0.124078 0.124202 0.121540 -24 0.020271 0.144348 0.144492 0.141425 -22 0.022295 0.166644 0.166806 0.163407 -20 0.024313 0.190957 0.191133 0.187495 -18 0.026284 0.217241 0.217426 0.213662 -16 0.028178 0.245418 0.245605 0.241841 -14 0.029952 0.275370 0.275552 0.271923 -12 0.031578 0.306948 0.307117 0.303758 -10 0.033015 0.339963 0.340115 0.337156 -8 0.034241 0.374204 0.374329 0.371890 -6 0.035220 0.409425 0.409519 0.407700 -4 0.035939 0.445364 0.445421 0.444299 -2 0.036374 0.481738 0.481759 0.481379 0 0.036523 0.518262 0.481759 0.481379

ROELEE 3.1 203

k, mk = 4 5 5 5 5 Sval P Cum P Stud T Normal -150 0.000000 0.000000 0.000000 0.000000 -148 0.000000 0.000000 0.000000 0.000000 -146 0.000000 0.000000 0.000000 0.000001 -144 0.000000 0.000000 0.000000 0.000001 -142 0.000000 0.000000 0.000000 0.000001 -140 0.000000 0.000000 0.000000 0.000001 -138 0.000000 0.000000 0.000000 0.000002 -136 0.000000 0.000000 0.000000 0.000003 -134 0.000000 0.000000 0.000000 0.000004 -132 0.000000 0.000000 0.000000 0.000005 -130 0.000000 0.000000 0.000001 0.000007 -128 0.000000 0.000001 0.000001 0.000010 -126 0.000001 0.000001 0.000002 0.000013 -124 0.000001 0.000002 0.000003 0.000017 -122 0.000001 0.000003 0.000004 0.000023 -120 0.000002 0.000005 0.000006 0.000031 -118 0.000003 0.000008 0.000010 0.000041 -116 0.000004 0.000013 0.000015 0.000055 -114 0.000006 0.000019 0.000021 0.000072 -112 0.000009 0.000028 0.000031 0.000094 -110 0.000013 0.000041 0.000044 0.000122 -108 0.000018 0.000059 0.000063 0.000159 -106 0.000025 0.000084 0.000088 0.000206 -104 0.000034 0.000118 0.000123 0.000265 -102 0.000046 0.000164 0.000169 0.000339 -100 0.000061 0.000225 0.000231 0.000433 -98 0.000080 0.000305 0.000312 0.000550 -96 0.000105 0.000411 0.000417 0.000696 -94 0.000136 0.000547 0.000554 0.000877 -92 0.000175 0.000722 0.000729 0.001100 -90 0.000223 0.000946 0.000952 0.001374 -88 0.000282 0.001228 0.001233 0.001710 -86 0.000354 0.001581 0.001586 0.002119 -84 0.000440 0.002021 0.002025 0.002614 -82 0.000543 0.002565 0.002566 0.003212 -80 0.000666 0.003231 0.003231 0.003930 -78 0.000811 0.004042 0.004040 0.004788 -76 0.000981 0.005023 0.005019 0.005810 -74 0.001179 0.006202 0.006195 0.007021 -72 0.001408 0.007610 0.007600 0.008450 -70 0.001670 0.009280 0.009268 0.010127 -68 0.001970 0.011250 0.011235 0.012089 -66 0.002309 0.013559 0.013542 0.014371 -64 0.002691 0.016250 0.016232 0.017015 -62 0.003118 0.019368 0.019349 0.020064 -60 0.003593 0.022962 0.022942 0.023565 -58 0.004118 0.027079 0.027060 0.027566 -56 0.004693 0.031773 0.031755 0.032117 -54 0.005321 0.037094 0.037079 0.037272 -52 0.006002 0.043096 0.043085 0.043084 -50 0.006735 0.049830 0.049824 0.049608 -48 0.007519 0.057349 0.057349 0.056896 -46 0.008352 0.065701 0.065708 0.065002 -44 0.009233 0.074934 0.074949 0.073978 -42 0.010156 0.085090 0.085115 0.083870 -40 0.011119 0.096209 0.096243 0.094725 -38 0.012115 0.108325 0.108369 0.106582 -36 0.013139 0.121464 0.121518 0.119474 -34 0.014184 0.135647 0.135712 0.133429 -32 0.015241 0.150888 0.150962 0.148466 -30 0.016302 0.167190 0.167273 0.164596 -28 0.017359 0.184549 0.184639 0.181820 -26 0.018402 0.202951 0.203046 0.200130 -24 0.019420 0.222371 0.222471 0.219505 -22 0.020405 0.242776 0.242878 0.239916 -20 0.021346 0.264122 0.264223 0.261320 -18 0.022233 0.286355 0.286454 0.283665 -14 0.023807 0.333217 0.333304 0.330910 -12 0.024476 0.357693 0.357771 0.355650 -10 0.025057 0.382750 0.382817 0.381015 -8 0.025541 0.408291 0.408345 0.406901

ROELEE 3.1 204

-6 0.025925 0.434216 0.434256 0.433201 -4 0.026202 0.460418 0.460442 0.459799 -2 0.026369 0.486787 0.486795 0.486580 0 0.026425 0.513213 0.486795 0.486580 k, mk = 5 2 2 2 2 2 Sval P Cum P Stud T Normal -40 0.000009 0.000009 0.000018 0.000185 -38 0.000035 0.000044 0.000064 0.000366 -36 0.000123 0.000168 0.000195 0.000699 -34 0.000309 0.000476 0.000516 0.001296 -32 0.000705 0.001182 0.001215 0.002328 -30 0.001384 0.002566 0.002596 0.004057 -28 0.002549 0.005115 0.005111 0.006855 -26 0.004277 0.009392 0.009376 0.011239 -24 0.006834 0.016226 0.016175 0.017882 -22 0.010229 0.026455 0.026430 0.027617 -20 0.014709 0.041164 0.041150 0.041419 -18 0.020097 0.061261 0.061350 0.060345 -16 0.026526 0.087787 0.087944 0.085452 -14 0.033545 0.121332 0.121641 0.117667 -12 0.041129 0.162460 0.162832 0.157651 -10 0.048563 0.211023 0.211504 0.205657 -8 0.055723 0.266746 0.267186 0.261408 -6 0.061764 0.328510 0.328935 0.324038 -4 0.066623 0.395132 0.395377 0.392096 -2 0.069533 0.464665 0.464787 0.463632 0 0.070670 0.535335 0.464787 0.463632 k, mk = 5 3 3 3 3 3 Sval P Cum P Stud T Normal -90 0.000000 0.000000 0.000000 0.000003 -88 0.000000 0.000000 0.000000 0.000005 -86 0.000000 0.000000 0.000000 0.000008 -84 0.000000 0.000000 0.000001 0.000013 -82 0.000001 0.000001 0.000002 0.000021 -80 0.000001 0.000002 0.000004 0.000032 -78 0.000003 0.000005 0.000007 0.000048 -76 0.000006 0.000011 0.000014 0.000073 -74 0.000011 0.000021 0.000026 0.000109 -72 0.000019 0.000040 0.000047 0.000162 -70 0.000032 0.000072 0.000081 0.000238 -68 0.000054 0.000126 0.000137 0.000346 -66 0.000086 0.000212 0.000226 0.000498 -64 0.000134 0.000345 0.000363 0.000711 -62 0.000203 0.000548 0.000569 0.001005 -60 0.000300 0.000848 0.000873 0.001406 -58 0.000434 0.001283 0.001310 0.001949 -56 0.000616 0.001898 0.001928 0.002676 -54 0.000856 0.002754 0.002786 0.003640 -52 0.001167 0.003921 0.003955 0.004905 -50 0.001565 0.005486 0.005521 0.006547 -48 0.002064 0.007549 0.007586 0.008658 -46 0.002679 0.010229 0.010268 0.011344 -44 0.003427 0.013656 0.013698 0.014726 -42 0.004322 0.017978 0.018024 0.018942 -40 0.005375 0.023352 0.023406 0.024143 -38 0.006598 0.029950 0.030012 0.030495 -36 0.007996 0.037946 0.038019 0.038173 -34 0.009571 0.047517 0.047605 0.047359 -32 0.011321 0.058838 0.058943 0.058237 -30 0.013237 0.072075 0.072199 0.070988 -28 0.015302 0.087377 0.087522 0.085782 -26 0.017495 0.104872 0.105038 0.102770 -24 0.019788 0.124660 0.124846 0.122080 -22 0.022145 0.146805 0.147008 0.143806 -20 0.024527 0.171332 0.171548 0.167999 -18 0.026889 0.198221 0.198445 0.194666 -16 0.029183 0.227405 0.227630 0.223760 -14 0.031360 0.258765 0.258984 0.255179 -12 0.033371 0.292136 0.292339 0.288761 -10 0.035166 0.327302 0.327482 0.324291

ROELEE 3.1 205

-8 0.036703 0.364005 0.364154 0.361498 -6 0.037942 0.401947 0.402059 0.400063 -4 0.038851 0.440798 0.440867 0.439629 -2 0.039406 0.480204 0.480227 0.479807 0 0.039593 0.519796 0.480227 0.479807 k, mk = 5 4 4 4 4 4 Sval P Cum P Stud T Normal -160 0.000000 0.000000 0.000000 0.000000 -158 0.000000 0.000000 0.000000 0.000000 -156 0.000000 0.000000 0.000000 0.000000 -154 0.000000 0.000000 0.000000 0.000000 -152 0.000000 0.000000 0.000000 0.000000 -150 0.000000 0.000000 0.000000 0.000000 -148 0.000000 0.000000 0.000000 0.000001 -146 0.000000 0.000000 0.000000 0.000001 -144 0.000000 0.000000 0.000000 0.000001 -142 0.000000 0.000000 0.000000 0.000001 -140 0.000000 0.000000 0.000000 0.000002 -138 0.000000 0.000000 0.000000 0.000003 -136 0.000000 0.000000 0.000000 0.000004 -134 0.000000 0.000000 0.000000 0.000005 -132 0.000000 0.000001 0.000001 0.000007 -130 0.000000 0.000001 0.000001 0.000009 -128 0.000001 0.000001 0.000002 0.000012 -126 0.000001 0.000002 0.000003 0.000017 -124 0.000001 0.000004 0.000004 0.000022 -122 0.000002 0.000006 0.000007 0.000029 -120 0.000003 0.000009 0.000010 0.000039 -118 0.000004 0.000013 0.000015 0.000051 -116 0.000006 0.000019 0.000021 0.000067 -114 0.000009 0.000028 0.000031 0.000087 -112 0.000012 0.000041 0.000043 0.000114 -110 0.000017 0.000058 0.000061 0.000147 -108 0.000023 0.000081 0.000085 0.000190 -106 0.000032 0.000113 0.000117 0.000244 -104 0.000042 0.000155 0.000161 0.000312 -102 0.000056 0.000211 0.000218 0.000398 -100 0.000074 0.000285 0.000292 0.000505 -98 0.000096 0.000381 0.000389 0.000638 -96 0.000124 0.000506 0.000514 0.000802 -94 0.000159 0.000665 0.000675 0.001006 -92 0.000203 0.000868 0.000878 0.001255 -90 0.000255 0.001123 0.001134 0.001560 -88 0.000320 0.001443 0.001454 0.001930 -86 0.000397 0.001841 0.001852 0.002380 -84 0.000490 0.002331 0.002342 0.002921 -82 0.000601 0.002932 0.002943 0.003572 -80 0.000731 0.003663 0.003674 0.004350 -78 0.000884 0.004547 0.004558 0.005276 -76 0.001063 0.005610 0.005621 0.006373 -74 0.001269 0.006879 0.006889 0.007667 -72 0.001506 0.008386 0.008396 0.009188 -70 0.001778 0.010163 0.010173 0.010966 -68 0.002086 0.012249 0.012259 0.013037 -66 0.002433 0.014682 0.014692 0.015437 -64 0.002822 0.017504 0.017515 0.018207 -62 0.003256 0.020760 0.020772 0.021390 -60 0.003736 0.024496 0.024510 0.025032 -58 0.004265 0.028762 0.028777 0.029179 -56 0.004844 0.033605 0.033624 0.033881 -54 0.005472 0.039078 0.039100 0.039190 -52 0.006152 0.045230 0.045256 0.045157 -50 0.006882 0.052111 0.052143 0.051835 -48 0.007660 0.059772 0.059809 0.059274 -46 0.008486 0.068258 0.068301 0.067526 -44 0.009356 0.077614 0.077664 0.076638 -42 0.010267 0.087881 0.087938 0.086657 -40 0.011214 0.099095 0.099160 0.097624 -38 0.012193 0.111288 0.111361 0.109575 -36 0.013197 0.124485 0.124564 0.122543 -34 0.014219 0.138703 0.138790 0.136551 -32 0.015251 0.153955 0.154048 0.151616 -30 0.016287 0.170242 0.170340 0.167747

ROELEE 3.1 206

-28 0.017317 0.187558 0.187660 0.184943 -26 0.018331 0.205890 0.205994 0.203195 -24 0.019321 0.225211 0.225317 0.222480 -22 0.020277 0.245488 0.245593 0.242769 -20 0.021190 0.266677 0.266780 0.264020 -18 0.022049 0.288726 0.288825 0.286180 -16 0.022846 0.311572 0.311665 0.309186 -14 0.023572 0.335145 0.335229 0.332966 -12 0.024220 0.359365 0.359439 0.357438 -10 0.024781 0.384145 0.384209 0.382510 -8 0.025249 0.409394 0.409445 0.408085 -6 0.025619 0.435013 0.435051 0.434058 -4 0.025887 0.460900 0.460923 0.460318 -2 0.026048 0.486949 0.486956 0.486753 0 0.026103 0.513051 0.486956 0.486753

ROELEE 3.1 207

k, mk = 5 5 5 5 5 5 Sval P Cum P Stud T Normal -250 0.000000 0.000000 0.000000 0.000000 -248 0.000000 0.000000 0.000000 0.000000 -246 0.000000 0.000000 0.000000 0.000000 -244 0.000000 0.000000 0.000000 0.000000 -242 0.000000 0.000000 0.000000 0.000000 -240 0.000000 0.000000 0.000000 0.000000 -238 0.000000 0.000000 0.000000 0.000000 -236 0.000000 0.000000 0.000000 0.000000 -234 0.000000 0.000000 0.000000 0.000000 -232 0.000000 0.000000 0.000000 0.000000 -230 0.000000 0.000000 0.000000 0.000000 -228 0.000000 0.000000 0.000000 0.000000 -226 0.000000 0.000000 0.000000 0.000000 -224 0.000000 0.000000 0.000000 0.000000 -222 0.000000 0.000000 0.000000 0.000000 -220 0.000000 0.000000 0.000000 0.000000 -218 0.000000 0.000000 0.000000 0.000000 -216 0.000000 0.000000 0.000000 0.000000 -214 0.000000 0.000000 0.000000 0.000000 -212 0.000000 0.000000 0.000000 0.000000 -210 0.000000 0.000000 0.000000 0.000000 -208 0.000000 0.000000 0.000000 0.000000 -206 0.000000 0.000000 0.000000 0.000000 -204 0.000000 0.000000 0.000000 0.000001 -202 0.000000 0.000000 0.000000 0.000001 -200 0.000000 0.000000 0.000000 0.000001 -198 0.000000 0.000000 0.000000 0.000001 -196 0.000000 0.000000 0.000000 0.000002 -194 0.000000 0.000000 0.000000 0.000002 -192 0.000000 0.000000 0.000000 0.000002 -190 0.000000 0.000000 0.000000 0.000003 -188 0.000000 0.000001 0.000001 0.000004 -186 0.000000 0.000001 0.000001 0.000005 -184 0.000000 0.000001 0.000001 0.000006 -182 0.000000 0.000001 0.000002 0.000008 -180 0.000000 0.000002 0.000002 0.000009 -178 0.000001 0.000003 0.000003 0.000012 -176 0.000001 0.000003 0.000004 0.000014 -174 0.000001 0.000005 0.000005 0.000018 -172 0.000001 0.000006 0.000007 0.000022 -170 0.000002 0.000008 0.000009 0.000027 -168 0.000003 0.000010 0.000011 0.000033 -166 0.000003 0.000014 0.000015 0.000040 -164 0.000004 0.000018 0.000019 0.000049 -162 0.000005 0.000023 0.000024 0.000059 -160 0.000007 0.000030 0.000031 0.000072 -158 0.000008 0.000038 0.000039 0.000087 -156 0.000010 0.000048 0.000050 0.000106 -154 0.000013 0.000061 0.000063 0.000127 -152 0.000016 0.000077 0.000079 0.000153 -150 0.000020 0.000097 0.000099 0.000184 -148 0.000024 0.000121 0.000124 0.000221 -146 0.000030 0.000151 0.000153 0.000264 -144 0.000036 0.000187 0.000190 0.000315 -142 0.000044 0.000230 0.000234 0.000375 -140 0.000053 0.000283 0.000287 0.000446 -138 0.000063 0.000346 0.000350 0.000528 -136 0.000076 0.000422 0.000426 0.000625 -134 0.000091 0.000513 0.000517 0.000738 -132 0.000108 0.000621 0.000625 0.000870 -130 0.000128 0.000749 0.000753 0.001022 -128 0.000151 0.000899 0.000904 0.001199 -126 0.000177 0.001077 0.001081 0.001404 -124 0.000208 0.001285 0.001289 0.001640 -122 0.000243 0.001528 0.001532 0.001911 -120 0.000283 0.001811 0.001815 0.002223 -118 0.000328 0.002139 0.002143 0.002580 -116 0.000380 0.002519 0.002523 0.002989 -114 0.000438 0.002957 0.002961 0.003454 -112 0.000503 0.003460 0.003464 0.003984 -110 0.000577 0.004037 0.004040 0.004586

ROELEE 3.1 208

-108 0.000659 0.004696 0.004698 0.005267 -106 0.000750 0.005446 0.005448 0.006037 -104 0.000852 0.006298 0.006299 0.006905 -102 0.000964 0.007262 0.007263 0.007881 -100 0.001088 0.008350 0.008351 0.008977 -98 0.001225 0.009575 0.009575 0.010204 -96 0.001375 0.010950 0.010950 0.011575 -94 0.001539 0.012489 0.012488 0.013104 -92 0.001717 0.014206 0.014205 0.014803 -90 0.001911 0.016117 0.016116 0.016689 -88 0.002121 0.018238 0.018237 0.018777 -86 0.002348 0.020587 0.020586 0.021082 -84 0.002592 0.023179 0.023178 0.023623 -82 0.002854 0.026033 0.026033 0.026417 -80 0.003135 0.029168 0.029169 0.029482 -78 0.003434 0.032602 0.032603 0.032836 -76 0.003751 0.036353 0.036356 0.036499 -74 0.004088 0.040441 0.040446 0.040489 -72 0.004444 0.044885 0.044891 0.044827 -70 0.004819 0.049704 0.049712 0.049531 -68 0.005212 0.054916 0.054926 0.054621 -66 0.005623 0.060539 0.060552 0.060116 -64 0.006052 0.066591 0.066607 0.066035 -62 0.006498 0.073090 0.073108 0.072396 -60 0.006960 0.080050 0.080071 0.079215 -58 0.007437 0.087487 0.087512 0.086511 -56 0.007928 0.095416 0.095444 0.094297 -54 0.008431 0.103847 0.103878 0.102588 -52 0.008945 0.112792 0.112827 0.111397 -50 0.009469 0.122261 0.122300 0.120734 -48 0.009999 0.132260 0.132302 0.130609 -46 0.010535 0.142796 0.142840 0.141029 -44 0.011074 0.153870 0.153918 0.151999 -42 0.011614 0.165484 0.165534 0.163521 -40 0.012153 0.177636 0.177689 0.175596 -38 0.012687 0.190324 0.190379 0.188221 -36 0.013215 0.203539 0.203596 0.201392 -34 0.013735 0.217274 0.217331 0.215100 -32 0.014242 0.231516 0.231574 0.229334 -30 0.014736 0.246252 0.246310 0.244082 -28 0.015212 0.261464 0.261521 0.259326 -26 0.015669 0.277133 0.277189 0.275049 -24 0.016104 0.293236 0.293291 0.291227 -22 0.016514 0.309751 0.309804 0.307835 -20 0.016898 0.326649 0.326699 0.324847 -18 0.017253 0.343901 0.343948 0.342233 -16 0.017576 0.361477 0.361519 0.359959 -14 0.017866 0.379343 0.379381 0.377992 -12 0.018121 0.397464 0.397497 0.396294 -10 0.018340 0.415804 0.415831 0.414829 -8 0.018521 0.434324 0.434346 0.433554 -6 0.018662 0.452987 0.453002 0.452431 -4 0.018764 0.471751 0.471761 0.471415 -2 0.018826 0.490577 0.490580 0.490464 0 0.018846 0.509423 0.490580 0.490464

ROELEE 3.1 209

k, mk = 6 2 2 2 2 2 2 Sval P Cum P Stud T Normal -60 0.000000 0.000000 0.000001 0.000020 -58 0.000001 0.000001 0.000002 0.000037 -56 0.000003 0.000003 0.000006 0.000065 -54 0.000008 0.000011 0.000016 0.000114 -52 0.000021 0.000032 0.000039 0.000194 -50 0.000047 0.000079 0.000090 0.000327 -48 0.000098 0.000177 0.000191 0.000539 -46 0.000189 0.000366 0.000384 0.000873 -44 0.000344 0.000710 0.000729 0.001390 -42 0.000590 0.001300 0.001318 0.002172 -40 0.000968 0.002267 0.002280 0.003335 -38 0.001518 0.003785 0.003791 0.005030 -36 0.002297 0.006082 0.006078 0.007454 -34 0.003353 0.009435 0.009422 0.010852 -32 0.004749 0.014184 0.014162 0.015527 -30 0.006525 0.020709 0.020687 0.021834 -28 0.008733 0.029443 0.029426 0.030181 -26 0.011386 0.040829 0.040833 0.041016 -24 0.014501 0.055330 0.055362 0.054810 -22 0.018039 0.073368 0.073445 0.072038 -20 0.021965 0.095333 0.095456 0.093141 -18 0.026179 0.121512 0.121689 0.118497 -16 0.030587 0.152099 0.152321 0.148379 -14 0.035030 0.187130 0.187392 0.182921 -12 0.039374 0.226503 0.226781 0.222085 -10 0.043423 0.269926 0.270205 0.265642 -8 0.047035 0.316962 0.317209 0.313155 -6 0.050024 0.366985 0.367185 0.363994 -4 0.052278 0.419263 0.419389 0.417348 -2 0.053665 0.472928 0.472974 0.472272 0 0.054144 0.527072 0.472974 0.472272 k, mk = 6 3 3 3 3 3 3 Sval P Cum P Stud T Normal -135 0.000000 0.000000 0.000000 0.000000 -133 0.000000 0.000000 0.000000 0.000000 -131 0.000000 0.000000 0.000000 0.000000 -129 0.000000 0.000000 0.000000 0.000000 -127 0.000000 0.000000 0.000000 0.000001 -125 0.000000 0.000000 0.000000 0.000001 -123 0.000000 0.000000 0.000000 0.000001 -121 0.000000 0.000000 0.000000 0.000002 -119 0.000000 0.000000 0.000000 0.000003 -117 0.000000 0.000000 0.000000 0.000004 -115 0.000000 0.000000 0.000000 0.000006 -113 0.000000 0.000001 0.000001 0.000008 -111 0.000000 0.000001 0.000001 0.000011 -109 0.000001 0.000002 0.000002 0.000016 -107 0.000001 0.000003 0.000004 0.000023 -105 0.000002 0.000005 0.000006 0.000031 -103 0.000003 0.000009 0.000010 0.000043 -101 0.000005 0.000014 0.000016 0.000059 -99 0.000008 0.000022 0.000025 0.000081 -97 0.000012 0.000034 0.000038 0.000110 -95 0.000018 0.000052 0.000056 0.000148 -93 0.000026 0.000079 0.000084 0.000199 -91 0.000037 0.000116 0.000122 0.000266 -89 0.000053 0.000169 0.000176 0.000353 -87 0.000073 0.000242 0.000251 0.000466 -85 0.000101 0.000343 0.000353 0.000612 -83 0.000137 0.000480 0.000491 0.000799 -81 0.000183 0.000663 0.000675 0.001038 -79 0.000242 0.000905 0.000919 0.001340 -77 0.000317 0.001222 0.001238 0.001721 -75 0.000411 0.001634 0.001651 0.002198 -73 0.000528 0.002162 0.002180 0.002792 -71 0.000671 0.002833 0.002852 0.003527 -69 0.000845 0.003678 0.003698 0.004431 -67 0.001054 0.004732 0.004753 0.005537

ROELEE 3.1 210

-65 0.001304 0.006036 0.006058 0.006882 -63 0.001599 0.007635 0.007658 0.008508 -61 0.001945 0.009581 0.009604 0.010461 -59 0.002347 0.011928 0.011953 0.012794 -57 0.002810 0.014738 0.014764 0.015564 -55 0.003338 0.018076 0.018104 0.018833 -53 0.003936 0.022012 0.022043 0.022670 -51 0.004608 0.026620 0.026655 0.027146 -49 0.005356 0.031976 0.032015 0.032336 -47 0.006182 0.038157 0.038202 0.038319 -45 0.007086 0.045243 0.045295 0.045174 -43 0.008069 0.053312 0.053371 0.052984 -41 0.009127 0.062439 0.062506 0.061829 -39 0.010257 0.072696 0.072771 0.071786 -37 0.011453 0.084149 0.084234 0.082928 -35 0.012709 0.096857 0.096952 0.095325 -33 0.014014 0.110872 0.110975 0.109034 -31 0.015359 0.126231 0.126344 0.124107 -29 0.016732 0.142963 0.143083 0.140579 -27 0.018118 0.161081 0.161208 0.158476 -25 0.019503 0.180584 0.180716 0.177806 -23 0.020871 0.201455 0.201590 0.198559 -21 0.022205 0.223659 0.223795 0.220709 -19 0.023488 0.247147 0.247281 0.244211 -17 0.024703 0.271850 0.271979 0.269000 -15 0.025834 0.297684 0.297804 0.294992 -13 0.026863 0.324547 0.324657 0.322084 -11 0.027777 0.352324 0.352420 0.350156 -9 0.028561 0.380885 0.380965 0.379072 -7 0.029203 0.410088 0.410150 0.408681 -5 0.029694 0.439782 0.439824 0.438821 -3 0.030026 0.469807 0.469829 0.469320 -1 0.030193 0.500000 0.500000 0.500000

ROELEE 3.1 211

k, mk = 6 4 4 4 4 4 4 Sval P Cum P Stud T Normal -240 0.000000 0.000000 0.000000 0.000000 -238 0.000000 0.000000 0.000000 0.000000 -236 0.000000 0.000000 0.000000 0.000000 -234 0.000000 0.000000 0.000000 0.000000 -232 0.000000 0.000000 0.000000 0.000000 -230 0.000000 0.000000 0.000000 0.000000 -228 0.000000 0.000000 0.000000 0.000000 -226 0.000000 0.000000 0.000000 0.000000 -224 0.000000 0.000000 0.000000 0.000000 -222 0.000000 0.000000 0.000000 0.000000 -220 0.000000 0.000000 0.000000 0.000000 -218 0.000000 0.000000 0.000000 0.000000 -216 0.000000 0.000000 0.000000 0.000000 -214 0.000000 0.000000 0.000000 0.000000 -212 0.000000 0.000000 0.000000 0.000000 -210 0.000000 0.000000 0.000000 0.000000 -208 0.000000 0.000000 0.000000 0.000000 -206 0.000000 0.000000 0.000000 0.000000 -204 0.000000 0.000000 0.000000 0.000000 -202 0.000000 0.000000 0.000000 0.000000 -200 0.000000 0.000000 0.000000 0.000000 -198 0.000000 0.000000 0.000000 0.000000 -196 0.000000 0.000000 0.000000 0.000000 -194 0.000000 0.000000 0.000000 0.000001 -192 0.000000 0.000000 0.000000 0.000001 -190 0.000000 0.000000 0.000000 0.000001 -188 0.000000 0.000000 0.000000 0.000001 -186 0.000000 0.000000 0.000000 0.000002 -184 0.000000 0.000000 0.000000 0.000002 -182 0.000000 0.000000 0.000000 0.000003 -180 0.000000 0.000000 0.000000 0.000003 -178 0.000000 0.000001 0.000001 0.000004 -176 0.000000 0.000001 0.000001 0.000005 -174 0.000000 0.000001 0.000001 0.000006 -172 0.000000 0.000001 0.000002 0.000008 -170 0.000001 0.000002 0.000002 0.000010 -168 0.000001 0.000003 0.000003 0.000013 -166 0.000001 0.000004 0.000004 0.000016 -164 0.000001 0.000005 0.000006 0.000020 -162 0.000002 0.000007 0.000008 0.000025 -160 0.000002 0.000009 0.000010 0.000031 -158 0.000003 0.000012 0.000013 0.000038 -156 0.000004 0.000017 0.000017 0.000047 -154 0.000005 0.000022 0.000023 0.000057 -152 0.000007 0.000028 0.000030 0.000070 -150 0.000008 0.000037 0.000038 0.000086 -148 0.000011 0.000047 0.000049 0.000105 -146 0.000014 0.000061 0.000063 0.000128 -144 0.000017 0.000078 0.000080 0.000156 -142 0.000021 0.000099 0.000102 0.000189 -140 0.000026 0.000125 0.000128 0.000229 -138 0.000032 0.000158 0.000161 0.000276 -136 0.000040 0.000198 0.000201 0.000333 -134 0.000049 0.000246 0.000250 0.000400 -132 0.000060 0.000306 0.000310 0.000479 -130 0.000072 0.000378 0.000383 0.000573 -128 0.000087 0.000466 0.000470 0.000683 -126 0.000105 0.000571 0.000575 0.000813 -124 0.000126 0.000696 0.000702 0.000965 -122 0.000150 0.000846 0.000852 0.001142 -120 0.000178 0.001025 0.001031 0.001349 -118 0.000211 0.001236 0.001242 0.001590 -116 0.000249 0.001485 0.001491 0.001870 -114 0.000293 0.001778 0.001784 0.002194 -112 0.000343 0.002121 0.002127 0.002568 -110 0.000400 0.002521 0.002527 0.002998 -108 0.000465 0.002985 0.002991 0.003492 -106 0.000538 0.003523 0.003529 0.004059 -104 0.000621 0.004144 0.004150 0.004706 -102 0.000714 0.004858 0.004863 0.005443 -100 0.000818 0.005676 0.005682 0.006282

ROELEE 3.1 212

-98 0.000935 0.006611 0.006616 0.007233 -96 0.001065 0.007676 0.007681 0.008309 -94 0.001208 0.008884 0.008889 0.009523 -92 0.001367 0.010251 0.010255 0.010890 -90 0.001542 0.011793 0.011797 0.012423 -88 0.001733 0.013526 0.013530 0.014141 -86 0.001942 0.015468 0.015473 0.016059 -84 0.002170 0.017638 0.017643 0.018196 -82 0.002418 0.020056 0.020061 0.020571 -80 0.002685 0.022742 0.022747 0.023204 -78 0.002974 0.025716 0.025722 0.026114 -76 0.003284 0.028999 0.029007 0.029324 -74 0.003615 0.032615 0.032623 0.032855 -72 0.003969 0.036584 0.036594 0.036729 -70 0.004345 0.040929 0.040941 0.040968 -68 0.004743 0.045673 0.045686 0.045597 -66 0.005164 0.050836 0.050852 0.050636 -64 0.005606 0.056442 0.056461 0.056110 -62 0.006069 0.062511 0.062533 0.062040 -60 0.006553 0.069064 0.069088 0.068448 -58 0.007056 0.076120 0.076147 0.075355 -56 0.007578 0.083698 0.083728 0.082781 -54 0.008116 0.091814 0.091848 0.090745 -52 0.008670 0.100483 0.100521 0.099263 -50 0.009237 0.109720 0.109761 0.108352 -48 0.009816 0.119536 0.119580 0.118025 -46 0.010403 0.129939 0.129987 0.128294 -44 0.010998 0.140937 0.140988 0.139166 -42 0.011597 0.152534 0.152588 0.150650 -40 0.012197 0.164732 0.164788 0.162748 -38 0.012796 0.177528 0.177587 0.175460 -36 0.013391 0.190919 0.190979 0.188785 -34 0.013978 0.204896 0.204958 0.202715 -32 0.014554 0.219450 0.219512 0.217242 -30 0.015116 0.234566 0.234628 0.232353 -28 0.015660 0.250226 0.250288 0.248032 -26 0.016185 0.266410 0.266472 0.264258 -24 0.016685 0.283095 0.283155 0.281007 -22 0.017159 0.300254 0.300311 0.298253 -20 0.017602 0.317856 0.317910 0.315966 -18 0.018013 0.335870 0.335920 0.334112 -16 0.018389 0.354259 0.354305 0.352654 -14 0.018727 0.372986 0.373027 0.371553 -12 0.019024 0.392010 0.392046 0.390767 -10 0.019280 0.411290 0.411320 0.410251 -8 0.019491 0.430781 0.430805 0.429960 -6 0.019657 0.450439 0.450456 0.449844 -4 0.019777 0.470215 0.470226 0.469856 -2 0.019849 0.490064 0.490067 0.489943 0 0.019873 0.509936 0.490067 0.489943

ROELEE 3.1 213

k, mk = 6 5 5 5 5 5 5 Sval P Cum P Stud T Normal -375 0.000000 0.000000 0.000000 0.000000 -373 0.000000 0.000000 0.000000 0.000000 -371 0.000000 0.000000 0.000000 0.000000 -369 0.000000 0.000000 0.000000 0.000000 -367 0.000000 0.000000 0.000000 0.000000 -365 0.000000 0.000000 0.000000 0.000000 -363 0.000000 0.000000 0.000000 0.000000 -361 0.000000 0.000000 0.000000 0.000000 -359 0.000000 0.000000 0.000000 0.000000 -357 0.000000 0.000000 0.000000 0.000000 -355 0.000000 0.000000 0.000000 0.000000 -353 0.000000 0.000000 0.000000 0.000000 -351 0.000000 0.000000 0.000000 0.000000 -349 0.000000 0.000000 0.000000 0.000000 -347 0.000000 0.000000 0.000000 0.000000 -345 0.000000 0.000000 0.000000 0.000000 -343 0.000000 0.000000 0.000000 0.000000 -341 0.000000 0.000000 0.000000 0.000000 -339 0.000000 0.000000 0.000000 0.000000 -337 0.000000 0.000000 0.000000 0.000000 -335 0.000000 0.000000 0.000000 0.000000 -333 0.000000 0.000000 0.000000 0.000000 -331 0.000000 0.000000 0.000000 0.000000 -329 0.000000 0.000000 0.000000 0.000000 -327 0.000000 0.000000 0.000000 0.000000 -325 0.000000 0.000000 0.000000 0.000000 -323 0.000000 0.000000 0.000000 0.000000 -321 0.000000 0.000000 0.000000 0.000000 -319 0.000000 0.000000 0.000000 0.000000 -317 0.000000 0.000000 0.000000 0.000000 -315 0.000000 0.000000 0.000000 0.000000 -313 0.000000 0.000000 0.000000 0.000000 -311 0.000000 0.000000 0.000000 0.000000 -309 0.000000 0.000000 0.000000 0.000000 -307 0.000000 0.000000 0.000000 0.000000 -305 0.000000 0.000000 0.000000 0.000000 -303 0.000000 0.000000 0.000000 0.000000 -301 0.000000 0.000000 0.000000 0.000000 -299 0.000000 0.000000 0.000000 0.000000 -297 0.000000 0.000000 0.000000 0.000000 -295 0.000000 0.000000 0.000000 0.000000 -293 0.000000 0.000000 0.000000 0.000000 -291 0.000000 0.000000 0.000000 0.000000 -289 0.000000 0.000000 0.000000 0.000000 -287 0.000000 0.000000 0.000000 0.000000 -285 0.000000 0.000000 0.000000 0.000000 -283 0.000000 0.000000 0.000000 0.000000 -281 0.000000 0.000000 0.000000 0.000000 -279 0.000000 0.000000 0.000000 0.000000 -277 0.000000 0.000000 0.000000 0.000000 -275 0.000000 0.000000 0.000000 0.000000 -273 0.000000 0.000000 0.000000 0.000000 -271 0.000000 0.000000 0.000000 0.000000 -269 0.000000 0.000000 0.000000 0.000001 -267 0.000000 0.000000 0.000000 0.000001 -265 0.000000 0.000000 0.000000 0.000001 -263 0.000000 0.000000 0.000000 0.000001 -261 0.000000 0.000000 0.000000 0.000001 -259 0.000000 0.000000 0.000000 0.000001 -257 0.000000 0.000000 0.000000 0.000002 -255 0.000000 0.000000 0.000000 0.000002 -253 0.000000 0.000000 0.000001 0.000002 -251 0.000000 0.000001 0.000001 0.000003 -249 0.000000 0.000001 0.000001 0.000003 -247 0.000000 0.000001 0.000001 0.000004 -245 0.000000 0.000001 0.000001 0.000005 -243 0.000000 0.000001 0.000002 0.000006 -241 0.000000 0.000002 0.000002 0.000007 -239 0.000000 0.000002 0.000002 0.000008 -237 0.000001 0.000003 0.000003 0.000009 -235 0.000001 0.000003 0.000004 0.000011

ROELEE 3.1 214

-233 0.000001 0.000004 0.000004 0.000013 -231 0.000001 0.000005 0.000005 0.000015 -229 0.000001 0.000006 0.000007 0.000018 -227 0.000001 0.000008 0.000008 0.000021 -225 0.000002 0.000010 0.000010 0.000024 -223 0.000002 0.000012 0.000012 0.000028 -221 0.000002 0.000014 0.000015 0.000033 -219 0.000003 0.000017 0.000018 0.000039 -217 0.000003 0.000020 0.000021 0.000045 -215 0.000004 0.000025 0.000025 0.000052 -213 0.000005 0.000030 0.000030 0.000061 -211 0.000006 0.000035 0.000036 0.000070 -209 0.000007 0.000042 0.000043 0.000081 -207 0.000008 0.000050 0.000051 0.000094 -205 0.000009 0.000060 0.000061 0.000108 -203 0.000011 0.000071 0.000072 0.000125 -201 0.000013 0.000084 0.000085 0.000144 -199 0.000015 0.000099 0.000100 0.000165 -197 0.000018 0.000116 0.000118 0.000190 -195 0.000020 0.000137 0.000138 0.000218 -193 0.000024 0.000160 0.000162 0.000249 -191 0.000027 0.000187 0.000189 0.000285 -189 0.000031 0.000219 0.000220 0.000326 -187 0.000036 0.000255 0.000256 0.000372 -185 0.000041 0.000296 0.000298 0.000425 -183 0.000047 0.000343 0.000345 0.000483 -181 0.000054 0.000398 0.000400 0.000550 -179 0.000062 0.000460 0.000462 0.000624 -177 0.000071 0.000530 0.000532 0.000708 -175 0.000080 0.000611 0.000613 0.000803 -173 0.000091 0.000702 0.000704 0.000908 -171 0.000103 0.000805 0.000807 0.001027 -169 0.000117 0.000921 0.000924 0.001159 -167 0.000132 0.001053 0.001055 0.001307 -165 0.000148 0.001201 0.001203 0.001471 -163 0.000167 0.001368 0.001370 0.001655 -161 0.000187 0.001555 0.001557 0.001859 -159 0.000209 0.001764 0.001766 0.002086 -157 0.000234 0.001998 0.002000 0.002338 -155 0.000261 0.002260 0.002262 0.002617 -153 0.000291 0.002551 0.002553 0.002925 -151 0.000324 0.002875 0.002877 0.003266 -149 0.000360 0.003235 0.003236 0.003643 -147 0.000399 0.003634 0.003635 0.004057 -145 0.000442 0.004076 0.004077 0.004514 -143 0.000488 0.004564 0.004565 0.005016 -141 0.000538 0.005103 0.005103 0.005567 -139 0.000593 0.005696 0.005695 0.006171 -137 0.000652 0.006347 0.006347 0.006833 -135 0.000716 0.007063 0.007062 0.007556 -133 0.000784 0.007848 0.007846 0.008346 -131 0.000858 0.008706 0.008704 0.009208 -129 0.000938 0.009643 0.009642 0.010146 -127 0.001023 0.010666 0.010664 0.011167 -125 0.001114 0.011780 0.011778 0.012277 -123 0.001211 0.012992 0.012989 0.013480 -121 0.001315 0.014307 0.014304 0.014784 -119 0.001426 0.015733 0.015730 0.016195 -117 0.001543 0.017276 0.017273 0.017720 -115 0.001668 0.018944 0.018941 0.019365 -113 0.001800 0.020744 0.020741 0.021139 -111 0.001940 0.022684 0.022681 0.023048 -109 0.002087 0.024772 0.024769 0.025100 -107 0.002243 0.027015 0.027012 0.027304 -105 0.002406 0.029421 0.029418 0.029666 -103 0.002578 0.031999 0.031996 0.032196 -101 0.002757 0.034756 0.034754 0.034901 -99 0.002946 0.037702 0.037700 0.037790 -97 0.003142 0.040844 0.040843 0.040871 -95 0.003347 0.044190 0.044191 0.044153 -93 0.003560 0.047750 0.047751 0.047644 -91 0.003781 0.051531 0.051533 0.051353 -89 0.004010 0.055541 0.055544 0.055288 -87 0.004248 0.059789 0.059793 0.059457 -85 0.004493 0.064282 0.064287 0.063869 -83 0.004745 0.069027 0.069034 0.068531

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-81 0.005006 0.074033 0.074041 0.073452 -79 0.005273 0.079305 0.079315 0.078638 -77 0.005546 0.084851 0.084863 0.084097 -75 0.005826 0.090678 0.090690 0.089836 -73 0.006112 0.096789 0.096804 0.095861 -71 0.006403 0.103192 0.103208 0.102179 -69 0.006699 0.109891 0.109909 0.108793 -67 0.006999 0.116890 0.116910 0.115710 -65 0.007303 0.124193 0.124214 0.122934 -63 0.007610 0.131803 0.131826 0.130468 -61 0.007919 0.139723 0.139747 0.138316 -59 0.008230 0.147953 0.147979 0.146480 -57 0.008542 0.156495 0.156522 0.154960 -55 0.008854 0.165350 0.165378 0.163759 -53 0.009166 0.174515 0.174545 0.172876 -51 0.009476 0.183991 0.184021 0.182310 -49 0.009783 0.193774 0.193806 0.192059 -47 0.010088 0.203862 0.203894 0.202121 -45 0.010388 0.214250 0.214283 0.212492 -43 0.010684 0.224934 0.224967 0.223167 -41 0.010974 0.235908 0.235941 0.234141 -39 0.011257 0.247164 0.247198 0.245407 -37 0.011532 0.258696 0.258730 0.256959 -35 0.011799 0.270495 0.270529 0.268787 -33 0.012057 0.282552 0.282585 0.280882 -31 0.012304 0.294856 0.294888 0.293235 -29 0.012541 0.307397 0.307428 0.305834 -27 0.012766 0.320163 0.320193 0.318667 -25 0.012978 0.333141 0.333169 0.331721 -23 0.013177 0.346318 0.346345 0.344982 -21 0.013362 0.359680 0.359705 0.358437 -19 0.013532 0.373212 0.373235 0.372070 -17 0.013687 0.386900 0.386921 0.385866 -15 0.013827 0.400727 0.400745 0.399807 -13 0.013950 0.414676 0.414693 0.413877 -11 0.014056 0.428733 0.428747 0.428058 -9 0.014146 0.442878 0.442889 0.442334 -7 0.014217 0.457096 0.457104 0.456684 -5 0.014271 0.471367 0.471373 0.471091 -3 0.014308 0.485674 0.485677 0.485536 -1 0.014326 0.500000 0.500000 0.500000 __________________________________________________________________

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Appendix 5E Jonckheere Module

subroutine Jonckcalc(result, fp, flev, factor 1 , N, NI, sortI2 1 , Trend8, rComp, rCompl, rP2Tl 1 , KWmode, JonckS, JonckChi2, JonckP, JonckPDir) c c work out trend probabilities via Jonckheere Test, JSF 21.12.94 c c result - result code, >0 if error c fp - field pointer of interest c flev - number of factor levels c factor - vector of factor values c c N = number of cases of interest after removing unwanted values c these cases have been sorted into ascending order c stored in sortI2 c NI= number of cases in each group c sortI2 - pointers to cases of interest in ascending order c Trend8 - trend values for each group c rComp,rCompl - details for ingored groups c KWmode = 0,1 for data in workI2/workR c = 2 for data in tempI2/tempR c c JonckS = Jonckheere S statistic, JSF 21.12.94 c JonckChi2 = Jonckheere S statistic transformed to approx Chi2 c JonckP = Prob of Jonckeere S statistic, JSF 21.12.94 c JonckPDir = Direction of Prob of Jonckheere S statistic, JSF 21.12.94 c c prob done exactly until pmax >300 then asymptotic value used c where pmax = (N*N - Sum ni*ni)/4 , maximum power of interest c Student T approximation will be used implicit integer*2 (a-z) parameter(mxJonckE=300 1 , maxprt=30) byte factor(*) integer*2 NI(*), sortI2(*) 1 , KWmode 1 , JonckS 1 , rComp, rCompl(*) 1 , k 1 , Sval(0:mxJonckE), pmax real*8 Sp(0:mxJonckE), ScumP(0:mxJonckE) 1 , JonckChi2 1 , JonckP, Pn 1 , ties 1 , XIN1, XINIc, BI, BN 1 , Pij(maxprt,maxprt) integer*2 sorttr(maxprt) 1 , trgrp (maxprt) 1 , INI (maxprt) 1 , mk (maxprt) 1 , nleft (maxprt) real*8 Trend8(*), TI, TN 1 , trscr(maxprt) 1 , small result = 0 JonckP = -1.0D0 JonckS = 0 small = 0.1E-10 ccc ! sort Trend8 into ascending order ccc ! put sorted order into sorttr k = 0 ! number of not ignored groups do 10 i=1, flev mk(i) = 0 ! holds no. cases in each group trgrp(i) = 0 ! holds pointers to groups of interest if(rComp.eq.-4) then

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ccc ingnore levels that have been marked as ignore if(rCompl(i).lt.0) go to 10 endif k = k +1 I1 = k TN = Trend8(i) 20 I1 = I1-1 if(I1.gt.0) then N1 = sorttr(I1) TI = Trend8(N1) if(TN.lt.TI) then sorttr(I1+1) = N1 go to 20 endif endif sorttr(I1+1) = i 10 continue ngrp = 0 TI = -99.0E5 ccc ! find any ties, put trends after matching ties into trscr ccc ! ngrp is number of different scores for use do i=1, k i1 = sorttr(i) TN = Trend8(i1) if(TN.gt.TI) ngrp = ngrp + 1 TI = TN trgrp(i1) = ngrp trscr(ngrp) = TI mk(ngrp) = mk(ngrp) + NI(i1) enddo if(ngrp.le.1) then result = 301 go to 99 endif do i=1, ngrp nleft(i) = mk(i) ! no. of cases not processed so far do j=1, ngrp Pij(i,j) = 0.0D0 enddo enddo i = 1 25 if(i.gt.N) go to 99 I1 = i IP = sortI2(i) IG = factor(ip) call valvs2(fp,KWmode,ip,v,BN) 30 continue ties = 0.0D0 ccc ! no. of tied obs ccc ! no of tied obs in group IG1 do ig1=1, ngrp INI(ig1) = 0 enddo 50 continue cS if(ostr.eq.istr) then ties = ties+1.0D0 INI(IG)= INI(IG) +1 cS endif 80 I1 = I1+1 if(i1.le.N) then IP1 = sortI2(i1) cS if(strlev.gt.0) then cS ostr = strata(ip1) cS if(ostr.ne.istr) go to 80 cS endif IG = factor(ip1) if(IG.lt.1 .or. IG.gt.flev) go to 80

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IG = trgrp(IG) if(IG.le.0) go to 80 call valvs2(fp,KWmode,ip1,v,BI) if(DABS(BI-BN).LT. small) go to 50 ccc ! tied ranks endif if(ties.gt. small) then ccc Jonckheere S statistic do ig1 = 1, ngrp INI1 = INI(ig1) if(INI1.gt.0) then do ig2 = ig1+1, ngrp INI2 = INI(ig2) if(INI2.gt.0) then Pij(ig1,ig2) = Pij(ig1,ig2) + INI1*INI2*0.5D0 Pij(ig2,ig1) = Pij(ig2,ig1) + INI1*INI2*0.5D0 endif enddo endif nleft(ig1) = nleft(ig1) - INI1 enddo do ig1 = 1, ngrp INI1 = INI(ig1) do ig2 = 1, ngrp if(ig1.ne.ig2) then Pij(ig1,ig2) = Pij(ig1,ig2) + INI1*nleft(ig2) endif enddo enddo endif I = I1 BN = BI IP = IP1 IF(I.le.N) go to 30 ccc Jonckheere S statistic JonckS = 0 do i=1, ngrp-1 do j=1+i, ngrp JonckS = JonckS + 2.0D0*Pij(i,j) - mk(i)*mk(j) enddo enddo ccc call asymptotic to get Chi2 approx call JonckAsym(mk, ngrp, JonckS, JonckChi2, JonckP, Pn, rP2Tl) ccc call exact via prob generating function call JonckPGF(mk, ngrp, Sval, Sp, ScumP, pmax) if(pmax.le.mxJonckE) then sv = -IABS(JonckS) do i=1, pmax if(sv.eq.Sval(i)) then JonckP = ScumP(i) if(rP2Tl.eq.0) then JonckP = 2.0D0*JonckP else if(rP2Tl.eq.1 .and. JonckS.lt.0) then JonckP = 1.0D0 - JonckP else if(rP2Tl.eq.-1 .and. JonckS.gt.0) then JonckP = 1.0D0 - JonckP endif go to 99 endif enddo endif 99 continue if(JonckS.ge.0) then JonckPDir = 1 else JonckPDir =-1 endif

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RETURN END subroutine mpolyn(A,B,C, maxp) ccc ccc routine to multiply together 2 polynomials, A and B ccc puttine the result into C ccc note, ABC are vectors starting at 0 where ccc 0 represents x**(0), ... i represents x**(i) ccc maxp is the maximum power we are interested in ccc implicit integer*2 (a-z) real*8 A(0:*), B(0:*), C(0:*) integer*2 maxp do i=0, maxp C(i) = A(0)*B(i) enddo do i=1, maxp do j=0, maxp - i C(i+j) = C(i+j) + A(i)*B(j) enddo enddo return end subroutine JonckPGF(mk, k, Sval, Sp, ScumP, pmax) ccc ccc routine to use Jonckheere Probability generating function ccc to calculate Probs for S statitic ccc ccc m1, ..., mk represent the number of cases in then k groups ccc f(m1,...,mk) = ccc (1/n!) X**{.5(n*n - Sum (mi*mi))} Prod (1 - X**(2s)) ccc --------------------------------------------------- ccc Prod {(1/mi!) Prod (1 - X**(2s))} ccc ccc n = Sum (mi) ccc ccc coefficients of Powers of X give Probs of S statistic ccc ccc values for S must run from - to + Smax = {.5(n*n - Sum (mi*mi)} ccc must be symetric, so we will just calc -ve values of S ccc Renaming X**2 as Y means we just need coeffs of Y ccc calculate Polynomial from ccc Prod( 1 - Y**s) * Prod Prod{1 + Y + Y*Y +... + Y**(s-1)} ccc s=1,n r=1,k s=1,mr ccc ignoring terms in Y to greater powers than ccc Smax/2 ccc ccc return results in Sval holding values of S ccc Sp probs of each S ccc ScumP cumulative probs of S ccc pmax number of values of S returned implicit integer*2 (a-z) parameter(mxJonckE=300) integer*2 mk(*), k 1 , Sval(0:*), pmax 1 , n, n2, n1, Smax, sv 1 , i, j, j1, r real*8 A(0:mxJonckE), B(0:mxJonckE), C(0:mxJonckE) real*8 Sp(0:*), ScumP(0:*) 1 , x n = 0 n2= 0 do i=1,k n = n + mk(i) n2 = n2 + mk(i)*mk(i) enddo

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Smax = (n*n - n2)/2 pmax = Smax /2 ! maximum power of interest if(pmax.gt.mxJonckE) go to 990 n1 = 0 x = 1.0D0 do i=1, k do j=1, mk(i) n1 = n1 +1 x = x*n1/j enddo enddo ccc ! do multiplication of polynomials A(0) = 1.0D0 B(0) = 1.0D0 C(0) = 1.0D0 do i=1, pmax B(i) = 0.0D0 C(i) = 0.0D0 enddo ccc ! start with Prod (1-Y**s), s=1, n C(1) = -1.0D0 do i=2, n if(i.gt.pmax) go to 10 do j=1, pmax A(j) = C(j) enddo B(i) = -1.0D0 call mpolyn(A,B,C,pmax) B(i) = 0.0D0 enddo 10 continue ccc ! now Prod over r=1,..,k, Prod(1-Y**s), s=1,...,mr do r=1,k do i=1, mk(r) do j=1, pmax A(j) = C(j) B(j) = 0.0D0 enddo do j=1, pmax j1 = i*j if(j1.gt.pmax) go to 30 B(j1) = 1.0D0 enddo 30 continue call mpolyn(A,B,C,pmax) enddo enddo ccc ! coefficients are now available in C ccc ! calculate probs by dividing by x sv = -Smax do i=0, pmax Sval(i) = sv sv = sv +2 Sp (i) = C(i)/x if(i.eq.0) then ScumP(i)= Sp(i) else ScumP(i)= ScumP(i-1) + Sp(i) endif enddo 990 continue return end subroutine JonckAsym(mk, k, S, x2, Pt, Pn, rP2Tl) ccc ccc routine to use Jonckheere Asymptotic Probability ccc to calculate Probs for S statitic ccc ccc m1, ..., mk represent the number of cases in the k groups ccc S = Jonckheere Statistic

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ccc x2 = chi squared approx ccc return results in Pt - prob from Student t ccc Pn - prob from Normal distribution ccc rP2Tl = 0) 2-sided, 1) 1-sided +ve 2) 1-sided -ve ccc ccc tv = S*SQRT{ v / {(v+1)u - S*S} ccc where t is Student t on v degrees of freedom ccc v = -3(2 +g)/g ccc ccc g = -(36/25) {n*n*n(6n*n+15n+10) - Sum{mr*mr*mr(6mr*mr+15mr+10)} ccc --------------------------------------------------- ccc {n*n(2n+3) - Sum{mr*mr(2mr+3)}**2 ccc ccc u = mean = (1/18){n*n(2n+3) - Sum{mr*mr(2mr+3)} ccc implicit integer*2 (a-z) integer*2 mk(*), k 1 , S 1 , df real*8 n, n2, n3, n4, n5, mk1, mk2, mk3, mk4, mk5 1 , m2, m3, m4, m5 real*8 Pt, Pn 1 , u1, u, g, v, S1, tv, x 1 , P, StudT, NProb 1 , x2 n = 0.0D0 m2 = 0.0D0 m3 = 0.0D0 m4 = 0.0D0 m5 = 0.0D0 do i=1,k mk1= mk(i) mk2 = mk1*mk1 mk3 = mk2*mk1 mk4 = mk3*mk1 mk5 = mk4*mk1 n = n + mk1 m2 = m2 + mk2 m3 = m3 + mk3 m4 = m4 + mk4 m5 = m5 + mk5 enddo n2 = n*n n3 = n2*n n4 = n3*n n5 = n4*n u1 = (2.0D0*(n3-m3)+(n2-m2)*3.0D0) u = u1/18.0D0 g = - (36.0D0/25.0D0) 1 * ( 6.0D0*(n5-m5) + 15.0D0*(n4-m4) + 10.0D0*(n3-m3) ) 1 / (u1*u1) v = -3.0D0*(2.0D0 +g)/g if(S.gt.0) then S1 = DFLOAT(S-1) ! take away 1 for continuity correction else if(S.lt.0) then S1 = DFLOAT(S+1) endif tv = S1*DSQRT( v / ((v+1.0D0)*u - S1*S1) ) ccc ! look up as Student T df = v + 0.5 ! round degrees of freedom to nearest integer P = StudT(tv, df) c c Two Sided Student t Probability 0 to abs(t) c if(rP2Tl.eq.0) then ! leave as 2-sided Pt = 1.0D0 - P else Pt = 0.5D0*(1.0D0 - P) ! get single sided tail P value if(rP2Tl.eq.1) then ! 1-sided +ve wanted if(S.le.0) Pt = 1.0D0 - Pt

ROELEE 3.1 222

else if(S.gt.0) Pt = 1.0D0 - Pt endif endif x = S1 / DSQRT(u) ! divide by mean P = Nprob(x) c function to calculate Cumulative Normal from -inf to x c if(rP2Tl.eq.0) then ! get 2-sided Pn = 2.0D0*(1.0D0 - P) else c ! get 1-sided +ve/-ve Pn = 1.0D0 - P if(rP2Tl.eq.1 .and. S.le.0) then Pn = P else if(rP2Tl.eq.-1 .and. S.gt.0) then Pn = P endif endif x2 = tv*tv return end __________________________________________________________________

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Appendix 6A Command File TEXACT.CMD

+ *** + *** Command File TEXACT.CMD + *** Used to test DATATOX F1 Statistics + *** Parametric Statistics - + *** Percent + *** Fisher Exact 1) Twice Minimum + *** 2) probs <= observed + *** Adjustments 1) Ahner-Passing + *** 2-5) Various Bonferronni Tests + *** Trend test via + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SEX 1 SELECT SET SEX 0 +SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 SET FACTOR GROUP .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 6B - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C: $36 5 :C: $36 6 :CO $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation

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$36 $36 further heading for group comparison analyses $36 11:L: $36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm $36 14TB: T T T T $36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 + *** MALES ONLY FOR SEX 1 .SET HEAD $136 6 :COMales $136 7 :COFor 2-tailed tests take twice minimum tail .SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? Y $14 2) Number of animals ? Y $14 3) Percentages ? Y $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? Y $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $14 EXACT SODIUM .SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? N $14 2) Number of animals ? N $14 3) Percentages ? N $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? N $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $14 + + Repeat for One-tailed +ve and -ve .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2

ROELEE 3.1 225

&EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &EXACT + + Now get probs using tails as sum probs <= observed + .SET HEAD $136 6 :COMales $136 7 :COFor 2-tailed tests take sum of probs <= observed .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET EXACT $114 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &EXACT + + Finally run through different Bonferonni adjustments .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET EXACT $114 4) Print probabilities ? N $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 2 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 3 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 4 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 5 &EXACT .SET EXACT $114 4) Print probabilities ? Y $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &EXACT /LUD &EXACT /LUD =4 + + *** TO CHECK LUDIN, RE-DO EXACT TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &EXACT .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &EXACT + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + *** REPEAT FOR FEMALES + *** FEMALES ONLY FOR SEX 2 .SET HEAD $136 6 :COFemales $136 7 :COFor 2-tailed tests take twice minimum tail

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.SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? Y $14 2) Number of animals ? Y $14 3) Percentages ? Y $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? Y $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $14 EXACT SODIUM .SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? N $14 2) Number of animals ? N $14 3) Percentages ? N $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? N $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $14 + + Repeat for One-tailed +ve and -ve .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &EXACT + + Now get probs using tails as sum probs <= observed + .SET HEAD $136 7 :COFor 2-tailed tests take sum of probs <= observed .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET EXACT $114 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &EXACT + + Finally run through different Bonferonni adjustments .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET EXACT $114 4) Print probabilities ? N $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 2 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 3 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 4 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 5 &EXACT .SET EXACT $114 4) Print probabilities ? Y $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &EXACT /LUD

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&EXACT /LUD =4 + + *** TO CHECK LUDIN, RE-DO EXACT TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &EXACT .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &EXACT + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + *** MALES + FEMALES FOR .SET HEAD $136 6 :COMales and Females $136 7 :COFor 2-tailed tests take twice minimum tail .SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? Y $14 2) Number of animals ? Y $14 3) Percentages ? Y $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? Y $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $14 EXACT SODIUM .SET EXACT $14 Fisher's Exact options $14 $14 1) Number of Positive values ? N $14 2) Number of animals ? N $14 3) Percentages ? N $14 4) Print probabilities ? Y $14 5) Minimum total positive ( or negative): 0 $14 6) Repeat analyses from maximum cut of: 0 $14 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 $14 8) Show totals over partitions ? Y $14 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 $14 10) Ahner-Passing Statistic ? N $14 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 $14 + + Repeat for One-tailed +ve and -ve .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &EXACT + + Now get probs using tails as sum probs <= observed +

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.SET HEAD $136 7 :COFor 2-tailed tests take sum of probs <= observed .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET EXACT $114 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &EXACT .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &EXACT + + Finally run through different Bonferonni adjustments .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 .SET EXACT $114 4) Print probabilities ? N $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 2 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 3 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 4 &EXACT .SET EXACT $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 5 &EXACT .SET EXACT $114 4) Print probabilities ? Y $114 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &EXACT /LUD &EXACT /LUD =4 + + *** TO CHECK LUDIN, RE-DO EXACT TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &EXACT .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &EXACT + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: WRITE ITEXACT __________________________________________________________________

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Appendix 6B Results from TEXACT.CMD

Appendix 6B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Males For 2-tailed tests take twice minimum tail + *** table generated : 24-FEB-95, 15:03:39 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 1 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 1 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Male Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Fisher's Exact options 1) Number of Positive values ? Y 2) Number of animals ? Y 3) Percentages ? Y 4) Print probabilities ? Y 5) Minimum total positive ( or negative): 0 6) Repeat analyses from maximum cut of: 0 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 8) Show totals over partitions ? Y 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 10) Ahner-Passing Statistic ? Y 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 1

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1 Appendix 6B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Males For 2-tailed tests take twice minimum tail Control 1 ppm 5 ppm 25 ppm Trend Sodium at 6 months (mmol/ l) ( > 146 ) n 10 4 5 0 N 10 10 10 10 % 100.000000 40.000000 50.000000 0.000000 P 0.010836 0.032508 0.000011 0.000059 AP S 2.652846 2.210705 4.421411 AP P 0.021932 0.070551 0.000030 ( > 146 ) P(+) 1.000000 1.000000 1.000000 0.999974 P(-) 0.005418 0.016254 0.000005 0.000030 For 2-tailed tests take sum of probs <= observed P 0.010836 0.032508 0.000011 0.000059 P(+) 1.000000 1.000000 1.000000 0.999974 P(-) 0.005418 0.016254 0.000005 0.000030 EB1 P 0.050000 0.100000 0.000032 EB2 P 0.050000 0.050000 0.001000 EB3 P 0.050000 0.050000 0.001000 EB4 P 0.050000 0.050000 0.001000 Control 1 ppm 5 ppm 25 ppm Ludin procedure with alpha set at 0.050000 P 0.000059 P 0.142436 P 0.010836 0.032508 Ludin procedure with alpha set at 0.001000 P 0.000059 P 0.142436 P 0.010836 0.032508 Group 4 removed Control 1 ppm 5 ppm 25 ppm Trend P 0.010836 0.032508 0.142436 Groups 3 and 4 removed P 0.010836 0.010836

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Appendix 6B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Females For 2-tailed tests take twice minimum tail + *** table generated : 24-FEB-95, 15:03:47 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 2 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 2 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Female Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Fisher's Exact options 1) Number of Positive values ? Y 2) Number of animals ? Y 3) Percentages ? Y 4) Print probabilities ? Y 5) Minimum total positive ( or negative): 0 6) Repeat analyses from maximum cut of: 0 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 8) Show totals over partitions ? Y 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 10) Ahner-Passing Statistic ? Y 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 1

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2 Appendix 6B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Females For 2-tailed tests take twice minimum tail Control 1 ppm 5 ppm 25 ppm Trend Sodium at 6 months (mmol/ l) ( > 146 ) n 3 2 7 6 N 9 10 10 10 % 33.333333 20.000000 70.000000 60.000000 P 0.888545 0.255277 0.484423 0.171523 AP S 0.574594 1.580135 1.149189 AP P 0.888922 0.262003 0.513592 P(+) 0.880805 0.127639 0.242211 0.085761 P(-) 0.444272 0.981478 0.948743 0.916101 For 2-tailed tests take sum of probs <= observed P 0.628483 0.178895 0.369850 0.171523 P(+) 0.880805 0.127639 0.242211 0.085761 P(-) 0.444272 0.981478 0.948743 0.916101 EB1 P 1.000000 1.000000 1.000000 EB2 P 1.000000 1.000000 1.000000 EB3 P 1.000000 1.000000 1.000000 EB4 P 1.000000 1.000000 1.000000 Control 1 ppm 5 ppm 25 ppm Ludin procedure with alpha set at 0.050000 P 0.171523 P 0.628483 0.178895 0.369850 Ludin procedure with alpha set at 0.001000 P 0.171523 P 0.628483 0.178895 0.369850 Group 4 removed Control 1 ppm 5 ppm 25 ppm Trend P 0.628483 0.178895 0.054468 Groups 3 and 4 removed P 0.628483 0.888545

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Appendix 6B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Males and Females For 2-tailed tests take twice minimum tail + *** table generated : 24-FEB-95, 15:03:58 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 3 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6 Fisher's Exact options 1) Number of Positive values ? Y 2) Number of animals ? Y 3) Percentages ? Y 4) Print probabilities ? Y 5) Minimum total positive ( or negative): 0 6) Repeat analyses from maximum cut of: 0 7) Treat not examined 1)Missing 2)Negative 3)Ignore group 1 8) Show totals over partitions ? Y 9) 2-tails 1)2xMimimum 2)Sum probs <= observed 1 10) Ahner-Passing Statistic ? Y 11) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 1

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3 Appendix 6B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Fisher's Exact Test Males and Females For 2-tailed tests take twice minimum tail Control 1 ppm 5 ppm 25 ppm Trend Sodium at 6 months (mmol/ l) ( > 146 ) n 13 6 12 6 N 19 20 20 20 % 68.421053 30.000000 60.000000 30.000000 P 0.036325 0.831685 0.036325 0.105951 AP S 2.388164 0.523433 2.388164 AP P 0.044925 0.914079 0.044925 P(+) 0.997095 0.810736 0.997095 0.949641 P(-) 0.018163 0.415842 0.018163 0.052976 For 2-tailed tests take sum of probs <= observed P 0.025645 0.741054 0.025645 0.105951 P(+) 0.997095 0.810736 0.997095 0.949641 P(-) 0.018163 0.415842 0.018163 0.052976 EB1 P 0.100000 1.000000 0.100000 EB2 P 0.100000 1.000000 0.100000 EB3 P 0.100000 1.000000 0.100000 EB4 P 0.100000 1.000000 0.100000 Control 1 ppm 5 ppm 25 ppm Ludin procedure with alpha set at 0.050000 P 0.105951 P 0.025645 0.741054 0.025645 Ludin procedure with alpha set at 0.001000 P 0.105951 P 0.025645 0.741054 0.025645 Group 4 removed Control 1 ppm 5 ppm 25 ppm Trend P 0.025645 0.741054 0.769263 Groups 3 and 4 removed P 0.025645 0.036325

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Appendix 6C Command File TCHI2.CMD

+ *** + *** Command File TCHI2.CMD + *** Used to test DATATOX F1 Statistics + *** Frequency Statistics - + *** + *** ChiSquared + *** + *** Adjustments 1) Ahner-Passing + *** 2-5) Various Bonferronni Tests + *** Trend test via + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SEX 1 SELECT SET SEX 0 +SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 SET FACTOR GROUP .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 6D - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C: $36 5 :C: $36 6 :CO $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation

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$36 $36 further heading for group comparison analyses $36 11:L: $36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm $36 14TB: T T T T $36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 + + *** Start with MALES FOR SEX 1 .SET HEAD $136 6 :COMales .SET CHI $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? Y $11 2) Expected Positive values ? Y $11 3) Expected values compared with control ? N $11 4) Number of animals ? Y $11 5) Mortality Ratio ? Y $11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print fatal(F) and incidental(I): 2 $11 CHI SODIUM .SET CHI $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? N $11 2) Expected Positive values ? N $11 3) Expected values compared with control ? N $11 4) Number of animals ? N $11 5) Mortality Ratio ? N $11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y

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$11 10) Print probabilities ? Y $11 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print fatal(F) and incidental(I): 2 $11 + + Repeat for One-tailed +ve and -ve .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &CHI .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &CHI + .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 + +*** USE LUDIN PROCEDURE +*** .SET chi $111 9) Chi-squared statistic ? Y $111 10) Print probabilities ? Y $114 20) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &CHI /LUD &CHI /LUD =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &CHI .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &CHI + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + *** REPEAT FOR FEMALES FOR SEX 2 .SET HEAD $136 6 :COFemales .SET CHI $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? Y $11 2) Expected Positive values ? Y $11 3) Expected values compared with control ? N $11 4) Number of animals ? Y $11 5) Mortality Ratio ? Y $11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y

ROELEE 3.1 238

$11 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print fatal(F) and incidental(I): 2 $11 CHI SODIUM .SET CHI $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? N $11 2) Expected Positive values ? N $11 3) Expected values compared with control ? N $11 4) Number of animals ? N $11 5) Mortality Ratio ? N $11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print fatal(F) and incidental(I): 2 $11 + + Repeat for One-tailed +ve and -ve .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &CHI .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &CHI + .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 + +*** USE LUDIN PROCEDURE +*** .SET chi $111 9) Chi-squared statistic ? Y $111 10) Print probabilities ? Y $114 20) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &CHI /LUD &CHI /LUD =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &CHI .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &CHI + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1

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$18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: + *** REPEAT FOR MALES + FEMALES FOR .SET HEAD $136 6 :COMales and Females .SET CHI $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? Y $11 2) Expected Positive values ? Y $11 3) Expected values compared with control ? N $11 4) Number of animals ? Y $11 5) Mortality Ratio ? Y $11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print fatal(F) and incidental(I): 2 $11 CHI SODIUM .SET CHI $11 Chi-squared, Peto and Visible options $11 $11 1) Number of Positive values ? N $11 2) Expected Positive values ? N $11 3) Expected values compared with control ? N $11 4) Number of animals ? N $11 5) Mortality Ratio ? N $11 6) Relative Risk ? N $11 7) Confidence levels for RR (give prob level): 0 $11 8) Compare RR over strata (heterogeneity) ? N $11 9) Chi-squared statistic ? Y $11 10) Print probabilities ? Y $11 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 $11 12) Minimum total positive ( or negative) 0 $11 13) Use missing data in fatal analyses ? Y $11 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 $11 15) Repeat analyses from maximum cut of: 0 $11 16) Show totals over partitions ? Y $11 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 $11 18) Fatality Condn: $11 19) Print fatal(F) and incidental(I): 2 $11 + + Repeat for One-tailed +ve and -ve .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 2 &CHI .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 3 &CHI + .SET PROB $117 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 + +*** USE LUDIN PROCEDURE +*** .SET chi $111 9) Chi-squared statistic ? Y $111 10) Print probabilities ? Y $114 20) Adjust Ps 0)No 1)AhnPas 2)Bonf 3)Holm 4)Hommel 5)Hochb 0 &CHI /LUD

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&CHI /LUD =4 + + *** TO CHECK LUDIN, RE-DO TESTS WITHOUT TOP DOSES .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 1 * $18 .SET HEAD $136 9 :COGroup 4 removed &CHI .SET CONT $18 Position of control group: * $18 Contr Low Middl High $18 0 1 * * $18 .SET HEAD $136 9 :COGroups 3 and 4 removed &CHI + + *** RESET CONTROLS .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET HEAD $136 9 :C: WRITE ITCHI __________________________________________________________________

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Appendix 6D Results from TCHI2.CMD

Appendix 6D - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Males + *** table generated : 24-FEB-95, 15:07:26 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 1 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 1 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Male Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Strata: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 6D - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Males Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? N 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? N 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 18) Fatality Condn: 19) Print fatal(F) and incidental(I): 2

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1 Appendix 6D - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Males Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 months (mmol/ l) ( > 146 ) n 10 4 5 0 19 E 4.750000 4.750000 4.750000 4.750000 19.000000 N 10 10 10 10 40 n/E 2.105263 0.842105 1.052632 0.000000 ChiSq 5.654762 4.053333 15.390000 19.842105 13.309950 P 0.017408 0.044084 0.000087 0.000183 0.000264 ( > 146 ) ChiSq 5.654762 4.053333 15.390000 19.842105 13.309950 P(+) 0.991296 0.977958 0.999956 0.000183 0.999868 ChiSq 5.654762 4.053333 15.390000 19.842105 13.309950 P(-) 0.008704 0.022042 0.000044 0.000183 0.000132 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 ChiSq 13.309950 ChiSq 2.408407 ChiSq 5.654762 4.053333 8.602871 P 0.000264 P 0.120685 P 0.017408 0.044084 0.013549 Ludin procedure with alpha set at 0.001000 ChiSq 13.309950 ChiSq 2.408407 ChiSq 5.654762 4.053333 8.602871 P 0.000264 P 0.120685 P 0.017408 0.044084 0.013549 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend ChiSq 5.654762 4.053333 8.602871 2.408407 P 0.017408 0.044084 0.013549 0.120685 Groups 3 and 4 removed ChiSq 5.654762 5.654762 8.142857 P 0.017408 0.017408 0.004323

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Appendix 6D - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Females + *** table generated : 24-FEB-95, 15:07:30 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 2 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 2 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Female Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Strata: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 6D - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Females Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? N 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? N 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 18) Fatality Condn: 19) Print fatal(F) and incidental(I): 2

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2 Appendix 6D - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 months (mmol/ l) ( > 146 ) n 3 2 7 6 18 E 4.153846 4.615385 4.615385 4.615385 18.000000 N 9 10 10 10 39 n/E 0.722222 0.433333 1.516667 1.300000 ChiSq 0.017857 1.227222 0.467222 6.242857 1.869507 P 0.893695 0.267948 0.494268 0.100374 0.171532 ChiSq 0.017857 1.227222 0.467222 6.242857 1.869507 P(+) 0.553153 0.133974 0.247134 0.100374 0.085766 ChiSq 0.017857 1.227222 0.467222 6.242857 1.869507 P(-) 0.446847 0.866026 0.752866 0.100374 0.914234 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 ChiSq 1.869507 ChiSq 0.017857 1.227222 0.467222 6.242857 P 0.171532 P 0.893695 0.267948 0.494268 0.100374 Ludin procedure with alpha set at 0.001000 ChiSq 1.869507 ChiSq 0.017857 1.227222 0.467222 6.242857 P 0.171532 P 0.893695 0.267948 0.494268 0.100374 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend ChiSq 0.017857 1.227222 5.311765 4.340913 P 0.893695 0.267948 0.070237 0.037207 Groups 3 and 4 removed ChiSq 0.017857 0.017857 0.411429 P 0.893695 0.893695 0.521245

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Appendix 6D - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Males and Females + *** table generated : 24-FEB-95, 15:07:34 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 3 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Strata: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 6D - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Males and Females Chi-squared, Peto and Visible options 1) Number of Positive values ? Y 2) Expected Positive values ? Y 3) Expected values compared with control ? N 4) Number of animals ? Y 5) Mortality Ratio ? Y 6) Relative Risk ? N 7) Confidence levels for RR (give prob level): 0 8) Compare RR over strata (heterogeneity) ? N 9) Chi-squared statistic ? Y 10) Print probabilities ? Y 11) Yates correction: 1)2x2 Tables 2)No 3)Trend also: 1 12) Minimum total positive ( or negative) 0 13) Use missing data in fatal analyses ? Y 14) Treat not examined 1)Missing 2)Negative 3)Ignore group 2 15) Repeat analyses from maximum cut of: 0 16) Show totals over partitions ? Y 17) Treat Observations: 1) Fatal 2) Incidental 3) Both ? 1 18) Fatality Condn: 19) Print fatal(F) and incidental(I): 2

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3 Appendix 6D - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Chi-Squared analysis Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Sodium at 6 months (mmol/ l) ( > 146 ) n 13 6 12 6 37 E 8.898734 9.367089 9.367089 9.367089 37.000000 N 19 20 20 20 79 n/E 1.460882 0.640541 1.281081 0.640541 ChiSq 4.211118 0.044643 4.211118 9.380289 2.690295 P 0.040160 0.832662 0.040160 0.024640 0.100961 ChiSq 4.211118 0.044643 4.211118 9.380289 2.690295 P(+) 0.979920 0.583669 0.979920 0.024640 0.949519 ChiSq 4.211118 0.044643 4.211118 9.380289 2.690295 P(-) 0.020080 0.416331 0.020080 0.024640 0.050481 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 ChiSq 2.690295 ChiSq 4.211118 0.044643 4.211118 9.380289 P 0.100961 P 0.040160 0.832662 0.040160 0.024640 Ludin procedure with alpha set at 0.001000 ChiSq 2.690295 ChiSq 4.211118 0.044643 4.211118 9.380289 P 0.100961 P 0.040160 0.832662 0.040160 0.024640 Group 4 removed Control 1 ppm 5 ppm 25 ppm Total Trend ChiSq 4.211118 0.044643 6.333859 0.124266 P 0.040160 0.832662 0.042133 0.724453 Groups 3 and 4 removed ChiSq 4.211118 4.211118 5.609474 P 0.040160 0.040160 0.017864

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Appendix 7A Command File TACOVA.CMD

.S 1.0 $(10X .C.... + *** + *** Command File TACOVA.CMD + *** Used to test DATATOX F1 Statistics + *** Regression and Covariance Statistics - + *** Based on Linear Modelling + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 FOR SEX 1 SELECT SET SEX 0 +SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 SET FACTOR GROUP .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 7B - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C: $36 5 :C: $36 6 :COMales $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation $36 $36 further heading for group comparison analyses $36 11:L:

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$36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm $36 14TB: T T T T $36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY /COVAR POTASS SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY /COVAR POTASS /LUDIN .SET ONEWAY $112 7) F statistic ? N

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$112 8) Print probabilities ? N &ONEWAY /REGR POTASS*@FACT &ONEWAY /REGR @FACT &ONEWAY /REGR @DOSE &ONEWAY /REGR POTASS*@DOSE + *** REPEAT ABOVE TESTS FOR FEMALES .SET HEAD $136 6 :COFemales FOR SEX 2 .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY /COVAR POTASS SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY /LUDIN /COVAR POTASS .SET ONEWAY $112 7) F statistic ? N $112 8) Print probabilities ? N &ONEWAY /REGR POTASS*@FACT &ONEWAY /REGR @FACT &ONEWAY /REGR @DOSE &ONEWAY /REGR POTASS*@DOSE + *** repeat for ALL with partition SEX FOR .SET HEAD $136 6 :COMales and Females SET PART SEX .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y

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$12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY /COVAR POTASS SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY /LUDIN /COVAR POTASS .SET ONEWAY $112 7) F statistic ? N $112 8) Print probabilities ? N &ONEWAY /REGR POTASS*@FACT &ONEWAY /REGR @FACT &ONEWAY /REGR @DOSE &ONEWAY /REGR POTASS*@DOSE + *** REPEAT ON ALL WITH NO PARTITION, BUT WITH SEX AS ADDITIONAL COVARIATE FOR SET PART 0 .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 ONEWAY /COVAR POTASS,SEX SODIUM .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n

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$12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? n $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 &ONEWAY /LUDIN /COVAR POTASS,SEX .SET ONEWAY $112 7) F statistic ? N $112 8) Print probabilities ? N &ONEWAY /REGR POTASS &ONEWAY /REGR POTASS*@FACT &ONEWAY /REGR SEX &ONEWAY /REGR SEX*@FACT &ONEWAY /REGR POTASS,SEX,@FACT,POTASS,POTASS.@FACT,SEX.@FACT &ONEWAY /REGR @FACT &ONEWAY /REGR @DOSE &ONEWAY /REGR POTASS*@DOSE &ONEWAY /REGR SEX*@DOSE &ONEWAY /REGR POTASS,SEX,@DOSE,POTASS.@DOSE,SEX.@DOSE WRITE ITCOVAR __________________________________________________________________

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Appendix 7B Results from TACOVA.CMD

Appendix 7B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males + *** table generated : 24-FEB-95, 15:09:06 Table number of next output: (0 for none) 1 Page numbers 1) First Page number: (0 for none) 1 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 1 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Male Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 7B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

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1 Appendix 7B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend ACOVA on Potassium at 6 months (mmol/l) Sodium at 6 N 10 10 10 10 40 months (mmol/ Mean 150.020000 144.940000 145.490000 142.870000 145.830000 l) GMean 150.010972 144.895886 145.443061 142.845482 145.775537 HMean 150.001988 144.851332 145.395380 142.820376 145.720509 St.Err 0.549909 1.186142 1.222152 0.871914 0.634956 St.Dev 1.738965 3.750911 3.864784 2.757233 4.015815 Var P 0.031708 0.026099 0.185860 0.114570 CoefV 1.159156 2.587906 2.656392 1.929889 2.753765 %dev -3.386215 -3.019597 -4.766031 F 13.022939 10.355665 25.798452 9.159348 14.413788 df 36 36 36 36 36 P 0.000928 0.002731 0.000012 0.000122 0.000543 COV P 0.001259 0.002068 0.000020 0.000180 0.002852 Control 1 ppm 5 ppm 25 ppm Total Ludin procedure with alpha set at 0.050000 F 10.212238 F 4.008149 F 11.345976 9.321174 7.047165 P 0.002852 P 0.055420 P 0.002366 0.005172 0.003586 Control 1 ppm 5 ppm 25 ppm Total Trend Model 1 628.944000 (39) Model 2 P 607.244386 (38) 0.251162 Constant P 136.613497 7.934371 0.000000 Potassium at P 2.522478 2.164668 0.251162 6 months (mmol/l) Model 3 P 346.758480 (35) 0.000180 Constant P 143.510962 6.576880 0.000000 Potassium at P 1.775515 1.773356 0.323594 6 months (mmol/l) factor Aliased -4.957489 -4.732409 -6.983102 1.412958 1.422092 1.417485 P 0.001259 0.002068 0.000020 Model 4 P 303.731056 (32) 0.230433 Constant P 165.782748 12.600677 0.000000 Potassium at Aliased 6 months (mmol/l) factor Aliased -22.802982 -35.894914 -38.554039 26.189032 16.622217 16.965579 P 0.390399 0.038415 0.029914 POTASS. -4.299713 0.544964 4.127557 4.378861 factor 3.426884 6.376904 2.856308 3.168626 P 0.218675 0.932429 0.158161 0.176561

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2 Appendix 7B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 1 628.944000 (39) Model 2 P 356.690000 (36) 0.000122 Constant P 150.020000 0.995392 0.000000 factor Aliased -5.080000 -4.530000 -7.150000 1.407697 1.407697 1.407697 P 0.000928 0.002731 0.000012 Model 1 628.944000 (39) Model 2 P 486.131386 (38) 0.001881 Constant P 147.275094 0.711962 0.000000 dose P -0.186464 0.055808 0.001881 Model 1 628.944000 (39) Model 2 P 607.244386 (38) 0.251162 Constant P 136.613497 7.934371 0.000000 Potassium at P 2.522478 2.164668 0.251162 6 months (mmol/l) Model 3 P 475.894460 (37) 0.002852 Constant P 140.847034 7.240538 0.000000 Potassium at P 1.746057 1.957168 0.378086 6 months (mmol/l) dose P -0.180218 0.056395 0.002852 Model 4 P 463.872437 (36) 0.340529 Constant P 147.114497 9.727407 0.000000 Potassium at P 0.027202 2.646523 0.991856 6 months (mmol/l) dose P -0.852714 0.698508 0.230111 POTASS. dose P 0.186933 0.193529 0.340529

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Appendix 7B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females + *** table generated : 24-FEB-95, 15:09:10 Table number of next output: (0 for none) 2 Page numbers 1) First Page number: (0 for none) 3 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : SEX 2 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Select Animals on field values Sex = Female Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 7B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

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3 Appendix 7B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend ACOVA on Potassium at 6 months (mmol/l) Sodium at 6 N 9 10 10 10 39 months (mmol/ Mean 145.644444 141.480000 144.690000 147.440000 144.792308 l) GMean 145.640452 141.371465 144.556446 147.429239 144.709346 HMean 145.636464 141.258390 144.418362 147.418456 144.622625 St.Err 0.381558 1.810021 2.037070 0.593146 0.777955 St.Dev 1.144674 5.723791 6.441782 1.875692 4.858329 Var P 0.000127 0.000052 0.179023 0.000011 CoefV 0.785937 4.045653 4.452127 1.272173 3.355378 %dev -2.859323 -0.655325 1.232835 F 4.046920 0.212575 0.752330 3.061807 4.736273 df 35 35 35 35 35 P 0.052001 0.647609 0.391648 0.040758 0.036368 COV P 0.159339 0.693931 0.737760 0.368379 0.317105 Control 1 ppm 5 ppm 25 ppm Total F 1.029252 F 2.070262 0.157520 0.113956 1.085520 P 0.317105 P 0.159339 0.693931 0.737760 0.368379 Control 1 ppm 5 ppm 25 ppm Total Trend Model 1 896.927692 (38) Model 2 P 640.592505 (37) 0.000455 Constant P 121.714510 6.034534 0.000000 Potassium at P 6.543323 1.700530 0.000455 6 months (mmol/l) Model 3 P 584.598914 (34) 0.368379 Constant P 127.507863 6.844185 0.000000 Potassium at P 5.113698 1.889990 0.010578 6 months (mmol/l) factor Aliased -2.831474 -0.756715 0.658610 1.967886 1.906621 1.951009 P 0.159339 0.693931 0.737760 Model 4 P 466.490914 (31) 0.068609 Constant P 153.639154 22.074282 0.000000 Potassium at Aliased 6 months (mmol/l) factor Aliased -44.109537 -33.868152 1.375622 24.304838 24.420957 26.106539 P 0.079235 0.175381 0.958315 POTASS. -2.254147 9.723184 7.103477 -2.009757 factor 6.213264 3.072687 2.957027 3.683804 P 0.719219 0.003471 0.022474 0.589269

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4 Appendix 7B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 1 896.927692 (38) Model 2 P 710.471222 (35) 0.040758 Constant P 145.644444 1.501820 0.000000 factor Aliased -4.164444 -0.954444 1.795556 2.070116 2.070116 2.070116 P 0.052001 0.647609 0.391648 Model 1 896.927692 (38) Model 2 P 800.785240 (37) 0.041896 Constant P 143.566994 0.944948 0.000000 dose P 0.154152 0.073139 0.041896 Model 1 896.927692 (38) Model 2 P 640.592505 (37) 0.000455 Constant P 121.714510 6.034534 0.000000 Potassium at P 6.543323 1.700530 0.000455 6 months (mmol/l) Model 3 P 622.786821 (36) 0.317105 Constant P 123.549417 6.297462 0.000000 Potassium at P 5.862320 1.827595 0.002809 6 months (mmol/l) dose P 0.071325 0.070304 0.317105 Model 4 P 538.770042 (35) 0.025333 Constant P 112.547384 7.580623 0.000000 Potassium at P 9.009600 2.187901 0.000222 6 months (mmol/l) dose P 1.637994 0.673869 0.020332 POTASS. dose P -0.425461 0.182114 0.025333

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Appendix 7B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females + *** table generated : 24-FEB-95, 15:09:14 Table number of next output: (0 for none) 3 Page numbers 1) First Page number: (0 for none) 5 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: F2 Sex Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

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Appendix 7B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

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5 Appendix 7B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Partitioned on Sex Control 1 ppm 5 ppm 25 ppm Total Trend ACOVA on Potassium at 6 months (mmol/l) Sodium at 6 months (mmol/l) Male N 10 10 10 10 40 Mean 150.020000 144.940000 145.490000 142.870000 145.830000 GMean 150.010972 144.895886 145.443061 142.845482 145.775537 HMean 150.001988 144.851332 145.395380 142.820376 145.720509 St.Err 0.549909 1.186142 1.222152 0.871914 0.634956 St.Dev 1.738965 3.750911 3.864784 2.757233 4.015815 Var P 0.031708 0.026099 0.185860 0.114570 CoefV 1.159156 2.587906 2.656392 1.929889 2.753765 %dev -3.386215 -3.019597 -4.766031 F 13.022939 10.355665 25.798452 9.159348 14.413788 df 36 36 36 36 36 P 0.000928 0.002731 0.000012 0.000122 0.000543 COV P 0.001259 0.002068 0.000020 0.000180 0.002852 Female N 9 10 10 10 39 Mean 145.644444 141.480000 144.690000 147.440000 144.792308 GMean 145.640452 141.371465 144.556446 147.429239 144.709346 HMean 145.636464 141.258390 144.418362 147.418456 144.622625 St.Err 0.381558 1.810021 2.037070 0.593146 0.777955 St.Dev 1.144674 5.723791 6.441782 1.875692 4.858329 Var P 0.000127 0.000052 0.179023 0.000011 CoefV 0.785937 4.045653 4.452127 1.272173 3.355378 %dev -2.859323 -0.655325 1.232835 F 4.046920 0.212575 0.752330 3.061807 4.736273 df 35 35 35 35 35 P 0.052001 0.647609 0.391648 0.040758 0.036368 COV P 0.159339 0.693931 0.737760 0.368379 0.317105 Control 1 ppm 5 ppm 25 ppm Total Male F 10.212238 F 4.008149 F 11.345976 9.321174 7.047165 P 0.002852 P 0.055420 P 0.002366 0.005172 0.003586 Female F 1.029252 F 2.070262 0.157520 0.113956 1.085520 P 0.317105 P 0.159339 0.693931 0.737760 0.368379

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6 Appendix 7B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Partitioned on Sex Control 1 ppm 5 ppm 25 ppm Total Trend Male Model 1 628.944000 (39) Model 2 P 607.244386 (38) 0.251162 Constant P 136.613497 7.934371 0.000000 Potassium at P 2.522478 2.164668 0.251162 6 months (mmol/l) Model 3 P 346.758480 (35) 0.000180 Constant P 143.510962 6.576880 0.000000 Potassium at P 1.775515 1.773356 0.323594 6 months (mmol/l) factor Aliased -4.957489 -4.732409 -6.983102 1.412958 1.422092 1.417485 P 0.001259 0.002068 0.000020 Model 4 P 303.731056 (32) 0.230433 Constant P 165.782748 12.600677 0.000000 Potassium at Aliased 6 months (mmol/l) factor Aliased -22.802982 -35.894914 -38.554039 26.189032 16.622217 16.965579 P 0.390399 0.038415 0.029914 POTASS. -4.299713 0.544964 4.127557 4.378861 factor 3.426884 6.376904 2.856308 3.168626 P 0.218675 0.932429 0.158161 0.176561 Female Model 1 896.927692 (38) Model 2 P 640.592505 (37) 0.000455 Constant P 121.714510 6.034534 0.000000 Potassium at P 6.543323 1.700530 0.000455 6 months (mmol/l) Model 3 P 584.598914 (34) 0.368379 Constant P 127.507863 6.844185 0.000000 Potassium at P 5.113698 1.889990 0.010578 6 months (mmol/l) factor Aliased -2.831474 -0.756715 0.658610 1.967886 1.906621 1.951009 P 0.159339 0.693931 0.737760 Model 4 P 466.490914 (31) 0.068609 Constant P 153.639154 22.074282 0.000000 Potassium at Aliased 6 months (mmol/l) factor Aliased -44.109537 -33.868152 1.375622 24.304838 24.420957 26.106539 P 0.079235 0.175381 0.958315 POTASS. -2.254147 9.723184 7.103477 -2.009757 factor 6.213264 3.072687 2.957027 3.683804 P 0.719219 0.003471 0.022474 0.589269

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7 Appendix 7B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Partitioned on Sex Control 1 ppm 5 ppm 25 ppm Total Trend Male Model 1 628.944000 (39) Model 2 P 356.690000 (36) 0.000122 Constant P 150.020000 0.995392 0.000000 factor Aliased -5.080000 -4.530000 -7.150000 1.407697 1.407697 1.407697 P 0.000928 0.002731 0.000012 Female Model 1 896.927692 (38) Model 2 P 710.471222 (35) 0.040758 Constant P 145.644444 1.501820 0.000000 factor Aliased -4.164444 -0.954444 1.795556 2.070116 2.070116 2.070116 P 0.052001 0.647609 0.391648 Male Model 1 628.944000 (39) Model 2 P 486.131386 (38) 0.001881 Constant P 147.275094 0.711962 0.000000 dose P -0.186464 0.055808 0.001881 Female Model 1 896.927692 (38) Model 2 P 800.785240 (37) 0.041896 Constant P 143.566994 0.944948 0.000000 dose P 0.154152 0.073139 0.041896 Male Model 1 628.944000 (39) Model 2 P 607.244386 (38) 0.251162 Constant P 136.613497 7.934371 0.000000 Potassium at P 2.522478 2.164668 0.251162 6 months (mmol/l) Model 3 P 475.894460 (37) 0.002852 Constant P 140.847034 7.240538 0.000000 Potassium at P 1.746057 1.957168 0.378086 6 months (mmol/l) dose P -0.180218 0.056395 0.002852 Model 4 P 463.872437 (36) 0.340529 Constant P 147.114497 9.727407 0.000000 Potassium at P 0.027202 2.646523 0.991856 6 months (mmol/l) dose P -0.852714 0.698508 0.230111 POTASS. dose P 0.186933 0.193529 0.340529

ROELEE 3.1 268

8 Appendix 7B - Table 3 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Partitioned on Sex Control 1 ppm 5 ppm 25 ppm Total Trend Female Model 1 896.927692 (38) Model 2 P 640.592505 (37) 0.000455 Constant P 121.714510 6.034534 0.000000 Potassium at P 6.543323 1.700530 0.000455 6 months (mmol/l) Model 3 P 622.786821 (36) 0.317105 Constant P 123.549417 6.297462 0.000000 Potassium at P 5.862320 1.827595 0.002809 6 months (mmol/l) dose P 0.071325 0.070304 0.317105 Model 4 P 538.770042 (35) 0.025333 Constant P 112.547384 7.580623 0.000000 Potassium at P 9.009600 2.187901 0.000222 6 months (mmol/l) dose P 1.637994 0.673869 0.020332 POTASS. dose P -0.425461 0.182114 0.025333

ROELEE 3.1 269

Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females + *** table generated : 24-FEB-95, 15:09:19 Table number of next output: (0 for none) 4 Page numbers 1) First Page number: (0 for none) 9 2) Page number: 1)Top or 2)Bottom 1 3) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 Choose animals 1) FOR : 2) *FOR : 3) SELECT : 4) Sex: 0)Ignore 1)Male 2)Female 3)M,F 4)I,M,F 0 Factor of interest: F3 Group FIELDS: (Cut-points if >0) F79(146) Sodium at 6 months (mmol/l) Partition: Include Trend statistic ? Y Contr Low Middl High 0 1 5 25 Include Row Totals ? Y Probability options 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 3) Filter results on Probs: 0) None or required level: 0 4) Number of Probability levels: 4 1 2 3 4 (*) * ** *** .1 .05 .01 .001 Position of control group: 1 Contr Low Middl High 0 0 0 0 Number of decimal places: 6

ROELEE 3.1 270

Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females One-way options 1) Number of animals ? Y 2) Mean Values ? Y 3) Confidence levels for Means (give prob level): 0 4) St.Errors ? Y 5) St.Deviations ? Y 6) Test variances: 0)No 1)Bartlett 2)Levene 1 7) F statistic ? Y 8) Print probabilities ? Y 9) Geometric Mean Values ? Y 10) Harmonic Mean Values ? Y 11) Coefficient of variation ? Y 12) Relative Group Mean difference ? Y 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 15) Degrees of freedom ? Y 16) Number of contrasts: 0

ROELEE 3.1 271

9 Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend ACOVA on Potassium at 6 months (mmol/l), Sex Sodium at 6 N 19 20 20 20 79 months (mmol/ Mean 147.947368 143.210000 145.090000 145.155000 145.317722 l) GMean 147.924613 143.122827 144.999076 145.119264 145.248211 HMean 147.901941 143.032301 144.905224 145.082993 145.176440 St.Err 0.612700 1.125468 1.159739 0.733610 0.501076 St.Dev 2.670699 5.033247 5.186511 3.280801 4.453658 Var P 0.009625 0.006857 0.387617 0.013558 CoefV 1.805168 3.514592 3.574685 2.260206 3.064773 %dev -3.202063 -1.931341 -1.887407 F 12.374555 4.501816 4.299329 4.183898 0.148515 df 75 75 75 75 75 P 0.000743 0.037162 0.041562 0.008558 0.701050 COV P 0.002741 0.018752 0.016766 0.015031 0.331890 Control 1 ppm 5 ppm 25 ppm Total F 0.953812 F 9.615792 5.779654 5.993063 3.722144 P 0.331890 P 0.002741 0.018752 0.016766 0.015031 Control 1 ppm 5 ppm 25 ppm Total Trend Model 1 1547.135190 (78) Model 2 P 1285.912045 (77) 0.000169 Constant P 126.696133 4.730772 0.000000 Potassium at P 5.185426 1.311109 0.000169 6 months (mmol/l) Model 1 1547.135190 (78) Model 2 P 1285.912045 (77) 0.000169 Constant P 126.696133 4.730772 0.000000 Potassium at P 5.185426 1.311109 0.000169 6 months (mmol/l) Model 3 P 1115.457047 (74) 0.014143 Constant P 130.593037 4.735425 0.000000 Potassium at P 4.807995 1.288527 0.000371 6 months (mmol/l) factor Aliased -3.929752 -3.023371 -3.085783 1.262493 1.244597 1.246285 P 0.002635 0.017560 0.015574

ROELEE 3.1 272

10 Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 4 P 1012.490116 (71) 0.074353 Constant P 153.311050 12.147509 0.000000 Potassium at Aliased 6 months (mmol/l) factor Aliased -41.382837 -28.505208 -18.624826 14.878325 14.368824 15.288180 P 0.006926 0.051143 0.227162 POTASS. -1.486001 9.089579 5.566454 2.852139 factor 3.356882 2.484162 2.093335 2.518486 P 0.659348 0.000483 0.009675 0.261242 Model 1 1547.135190 (78) Model 2 P 1525.871692 (77) 0.303507 Constant P 145.830000 0.703856 0.000000 Sex 1 Aliased 2 P -1.037692 1.001763 0.303507 Model 1 1547.135190 (78) Model 2 P 1525.871692 (77) 0.303507 Constant P 145.830000 0.703856 0.000000 Sex 1 Aliased 2 P -1.037692 1.001763 0.303507 Model 3 P 1306.701160 (74) 0.009093 Constant P 148.407600 1.063071 0.000000 Sex 1 Aliased 2 P -0.971600 0.945874 0.307673 factor Aliased -4.711800 -2.831800 -2.766800 1.346440 1.346440 1.346440 P 0.000793 0.038850 0.043419 Model 4 P 1067.161222 (71) 0.002323 Constant P 150.020000 1.225987 0.000000 Sex 1 Aliased 2 Aliased factor Aliased Aliased Aliased Aliased P SEX. factor 1 Aliased 2 P -5.080000 1.733807 0.004556 3 P -4.530000 1.733807 0.010956 4 P -7.150000 1.733807 0.000100 5 P -4.375556 1.781318 0.016483 6 P -8.540000 1.733807 0.000005 7 P -5.330000 1.733807 0.002995 8 P -2.580000 1.733807 0.141165

ROELEE 3.1 273

11 Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 1 1547.135190 (78) Model 2 P 1285.912045 (77) 0.000169 Constant P 126.696133 4.730772 0.000000 Potassium at P 5.185426 1.311109 0.000169 6 months (mmol/l) Model 3 P 1282.963594 (76) 0.677182 Constant P 127.253808 4.939969 0.000000 Potassium at P 5.084144 1.340285 0.000296 6 months (mmol/l) Sex 1 Aliased 2 P -0.392886 0.940091 0.677182 Model 4 P 1112.751708 (73) 0.015031 Constant P 131.145371 4.939152 0.000000 Potassium at P 4.704425 1.318864 0.000642 6 months (mmol/l) Sex 1 Aliased 2 P -0.376835 0.894496 0.674787 factor Aliased -3.937232 -3.009878 -3.069545 1.269692 1.251982 1.253862 P 0.002741 0.018752 0.016766 Model 5 P 1012.418055 (70) 0.083517 Constant P 153.445141 12.380153 0.000000 Potassium at Aliased 6 months (mmol/l) Sex 1 Aliased 2 P -0.064283 0.910713 0.943929 factor Aliased -41.335918 -28.509263 -18.830149 14.998425 14.470694 15.668819 P 0.007454 0.052780 0.233507 POTASS. -1.514715 9.046322 5.539589 2.880302 factor 3.405041 2.575720 2.142240 2.567513 P 0.657804 0.000783 0.011796 0.265770

ROELEE 3.1 274

12 Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 6 P 815.448449 (67) 0.002191 Constant P 163.342823 11.736667 0.000000 Potassium at Aliased 6 months (mmol/l) Sex 1 Aliased 2 Aliased factor Aliased Aliased Aliased Aliased P POTASS. -3.634158 8.550773 5.903147 0.930267 factor 3.187317 2.580845 2.054169 2.434076 P 0.258265 0.001490 0.005430 0.703534 SEX. factor 1 Aliased 2 P -49.159954 15.004868 0.001668 3 P -40.166718 14.115874 0.005877 4 P -23.795735 14.647906 0.108962 5 P -4.809232 1.647445 0.004775 6 P -49.960663 14.521982 0.001004 7 P -39.361062 13.816412 0.005822 8 P -19.408998 14.937515 0.198279 Model 1 1547.135190 (78) Model 2 P 1325.332868 (75) 0.008558 Constant P 147.947368 0.964395 0.000000 factor Aliased -4.737368 -2.857368 -2.792368 1.346705 1.346705 1.346705 P 0.000743 0.037162 0.041562 Model 1 1547.135190 (78) Model 2 P 1544.510770 (77) 0.718556 Constant P 145.458518 0.636725 0.000000 dose P -0.017940 0.049598 0.718556 Model 1 1547.135190 (78) Model 2 P 1285.912045 (77) 0.000169 Constant P 126.696133 4.730772 0.000000 Potassium at P 5.185426 1.311109 0.000169 6 months (mmol/l) Model 3 P 1269.299199 (76) 0.321760 Constant P 126.346135 4.743932 0.000000 Potassium at P 5.382646 1.325982 0.000118 6 months (mmol/l) dose P -0.045647 0.045769 0.321760

ROELEE 3.1 275

13 Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 4 P 1252.785812 (75) 0.323282 Constant P 122.513879 6.112594 0.000000 Potassium at P 6.456996 1.710564 0.000318 6 months (mmol/l) dose P 0.448018 0.498608 0.371776 POTASS. dose P -0.135825 0.136606 0.323282 Model 1 1547.135190 (78) Model 2 P 1525.871692 (77) 0.303507 Constant P 145.830000 0.703856 0.000000 Sex 1 Aliased 2 P -1.037692 1.001763 0.303507 Model 3 P 1523.391105 (76) 0.725972 Constant P 145.965179 0.805466 0.000000 Sex 1 Aliased 2 P -1.034226 1.007560 0.307928 dose P -0.017442 0.049583 0.725972 Model 4 P 1286.916627 (75) 0.000392 Constant P 147.275094 0.824549 0.000000 Sex 1 Aliased 2 P -3.708100 1.178054 0.002362 dose Aliased SEX. dose 1 P -0.186464 0.064633 0.005108 2 P 0.154152 0.065123 0.020510 Model 1 1547.135190 (78) Model 2 P 1285.912045 (77) 0.000169 Constant P 126.696133 4.730772 0.000000 Potassium at P 5.185426 1.311109 0.000169 6 months (mmol/l) Model 3 P 1282.963594 (76) 0.677182 Constant P 127.253808 4.939969 0.000000 Potassium at P 5.084144 1.340285 0.000296 6 months (mmol/l) Sex 1 Aliased 2 P -0.392886 0.940091 0.677182 Model 4 P 1266.852400 (75) 0.331890 Constant P 126.859599 4.957929 0.000000 Potassium at P 5.287454 1.356758 0.000210 6 months (mmol/l) Sex 1 Aliased 2 P -0.358161 0.941049 0.704577 dose P -0.044985 0.046061 0.331890

ROELEE 3.1 276

14 Appendix 7B - Table 4 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males and Females Sodium at 6 months (mmol/l) Control 1 ppm 5 ppm 25 ppm Total Trend Model 5 P 1252.576914 (74) 0.361418 Constant P 122.794197 6.650524 0.000000 Potassium at P 6.393236 1.815073 0.000737 6 months (mmol/l) Sex 1 Aliased 2 P -0.108909 0.980352 0.911845 dose P 0.432222 0.521676 0.410037 POTASS. dose P -0.131424 0.143108 0.361418 Model 6 P 1106.228059 (73) 0.002687 Constant P 126.283913 6.392016 0.000000 Potassium at P 5.717827 1.731086 0.001483 6 months (mmol/l) Sex 1 Aliased 2 P -2.350271 1.174993 0.049194 dose Aliased POTASS. dose P -0.181937 0.136379 0.186332 SEX. dose 1 P 0.482527 0.493865 0.331775 2 P 0.762327 0.504900 0.135397

ROELEE 3.1 277

Appendix 7C GLIM Batch File

$! TGLIM.COM $! COMMAND FILE TO CHECK REGRESSION/COVARIANCE $! IN DATATOX F1 STATISTICS BY RUNNING THE SAME $! ANALYSES IN GLIM $! JSF 23.1.95 $! $ SET DEF [RLINSTEM.RLITEST] $ ASSIGN VLIST.DAT FOR010 $ GLIMB OUTPUT=TGLIM.DAT &OUTPUT 8 &UNIT 80 &FACTOR GP 4 SEX 2 &DATA REF I SEX GP SOD POT &DINP 10 & &CALC DOSE = %IF( %EQ(GP,1),0, %IF( %EQ(GP,2),1, %IF( %EQ(GP,3),5,25))) &YVAR SOD &CALC W1=%IF(%EQ(SEX,2),0,1) &WEI W1 &FIT &DIS EM &FIT POT &DIS E &FIT GP &DIS E &FIT DOSE &DIS E &FIT POT+GP &DIS E &FIT POT*GP &DIS E &FIT POT+DOSE &DIS E &CALC W2=%IF(%EQ(SEX,1),0,1) &CALC W2=%IF(%LT(POT,0),0,W2) &WEI W2 &FIT &DIS EM &FIT POT &DIS E &FIT GP &DIS E &FIT DOSE &DIS E &FIT POT+GP &DIS E &FIT POT*GP &DIS E &FIT POT+DOSE &DIS E &CALC W3=%IF(%LT(POT,0),0,1) &WEI W3 &FIT &DIS EM &FIT POT &DIS E &FIT GP &DIS E &FIT DOSE &DIS E &FIT POT+GP &DIS E &FIT POT*GP &DIS E &FIT POT+DOSE &DIS E &FIT SEX &DIS E &FIT SEX+POT &DIS E &FIT SEX+POT+GP &DIS E &FIT SEX*GP &DIS E &FIT SEX*GP +POT*GP &DIS E &STOP __________________________________________________________________

ROELEE 3.1 278

Appendix 7D Results from GLIM Batch File

&DATA REF I SEX GP SOD POT &DINP 10 & 1 1 1 1 150.0 3.82 2 1 1 1 148.1 3.93 3 1 1 1 150.3 3.79 4 1 1 1 149.9 3.80 5 1 1 1 150.6 3.25 6 1 1 1 153.2 3.31 7 1 1 1 148.3 4.17 8 1 1 1 152.5 3.34 9 1 1 1 148.9 3.53 10 1 1 1 148.4 3.72 11 1 2 1 145.3 3.68 12 1 2 1 147.4 3.52 13 1 2 1 145.1 3.36 14 1 2 1 -4 -4 15 1 2 1 145.7 3.25 16 1 2 1 144.5 3.55 17 1 2 1 146.3 3.50 18 1 2 1 147.2 3.52 19 1 2 1 145.3 3.50 20 1 2 1 144.0 4.04 21 1 1 2 145.9 3.56 22 1 1 2 147.6 3.53 23 1 1 2 150.9 3.76 24 1 1 2 145.5 3.80 25 1 1 2 146.9 3.36 26 1 1 2 146.6 3.57 27 1 1 2 143.8 3.34 28 1 1 2 144.1 3.77 29 1 1 2 140.6 3.68 30 1 1 2 137.5 3.60 31 1 2 2 147.9 3.51 32 1 2 2 145.4 3.78 33 1 2 2 141.5 3.29 34 1 2 2 141.8 3.19 35 1 2 2 138.0 2.60 36 1 2 2 142.9 3.37 37 1 2 2 127.4 2.86 38 1 2 2 140.9 3.09 39 1 2 2 142.6 3.13 40 1 2 2 146.4 4.04 41 1 1 3 138.0 3.41 42 1 1 3 139.8 3.60 43 1 1 3 147.9 3.53 44 1 1 3 146.7 3.47 45 1 1 3 145.8 3.73 46 1 1 3 145.3 4.59 47 1 1 3 144.5 3.61 48 1 1 3 149.9 4.08 49 1 1 3 148.5 4.02 50 1 1 3 148.5 3.76 51 1 2 3 134.4 3.46 52 1 2 3 132.1 2.77 53 1 2 3 142.2 3.79 54 1 2 3 148.9 4.37 55 1 2 3 147.1 3.43 56 1 2 3 149.5 3.35 57 1 2 3 150.2 3.85 58 1 2 3 146.3 3.42 59 1 2 3 148.1 3.57 60 1 2 3 148.1 3.07 61 1 1 4 141.8 3.58 62 1 1 4 143.8 3.87 63 1 1 4 145.4 3.57 64 1 1 4 135.7 3.07 65 1 1 4 145.1 3.40 66 1 1 4 143.6 4.20 67 1 1 4 144.4 3.64 68 1 1 4 142.4 3.20 69 1 1 4 143.6 3.46 70 1 1 4 142.9 3.73

ROELEE 3.1 279

71 1 2 4 149.3 3.40 72 1 2 4 148.5 4.24 73 1 2 4 147.4 3.55 74 1 2 4 149.4 3.61 75 1 2 4 144.4 4.41 76 1 2 4 149.7 3.68 77 1 2 4 148.3 3.77 78 1 2 4 145.8 4.05 79 1 2 4 145.6 3.60 80 1 2 4 146.0 3.38 &CALC DOSE = %IF( %EQ(GP,1),0, %IF( %EQ(GP,2),1, %IF( %EQ(GP,3),5,25))) &YVAR SOD &CALC W1=%IF(%EQ(SEX,2),0,1) &WEI W1 &FIT &DIS EM CYCLE DEVIANCE DF 1 628.9 39 ESTIMATE S.E. PARAMETER 1 145.8 0.6350 %GM SCALE PARAMETER TAKEN AS 16.13 Y-VARIATE SOD ERROR NORMAL LINK IDENTITY WEIGHT W1 LINEAR PREDICTOR %GM &FIT POT &DIS E CYCLE DEVIANCE DF 1 607.2 38 ESTIMATE S.E. PARAMETER 1 136.6 7.934 %GM 2 2.522 2.165 POT SCALE PARAMETER TAKEN AS 15.98 &FIT GP &DIS E CYCLE DEVIANCE DF 1 356.7 36 ESTIMATE S.E. PARAMETER 1 150.0 0.9954 %GM 2 -5.080 1.408 GP(2) 3 -4.530 1.408 GP(3) 4 -7.150 1.408 GP(4) SCALE PARAMETER TAKEN AS 9.908 &FIT DOSE &DIS E CYCLE DEVIANCE DF 1 486.1 38 ESTIMATE S.E. PARAMETER 1 147.3 0.7120 %GM 2 -0.1865 0.5581E-01 DOSE SCALE PARAMETER TAKEN AS 12.79 &FIT POT+GP &DIS E CYCLE DEVIANCE DF 1 346.8 35 ESTIMATE S.E. PARAMETER 1 143.5 6.577 %GM 2 1.776 1.773 POT 3 -4.957 1.413 GP(2) 4 -4.732 1.422 GP(3) 5 -6.983 1.417 GP(4) SCALE PARAMETER TAKEN AS 9.907 &FIT POT*GP &DIS E CYCLE DEVIANCE DF 1 303.7 32

ROELEE 3.1 280

ESTIMATE S.E. PARAMETER 1 165.8 12.60 %GM 2 -4.300 3.427 POT 3 -22.80 26.19 GP(2) 4 -35.89 16.62 GP(3) 5 -38.55 16.97 GP(4) 6 4.845 7.239 POT.GP(2) 7 8.427 4.461 POT.GP(3) 8 8.679 4.667 POT.GP(4) SCALE PARAMETER TAKEN AS 9.492 &FIT POT+DOSE &DIS E CYCLE DEVIANCE DF 1 475.9 37 ESTIMATE S.E. PARAMETER 1 140.8 7.241 %GM 2 1.746 1.957 POT 3 -0.1802 0.5639E-01 DOSE SCALE PARAMETER TAKEN AS 12.86 &CALC W2=%IF(%EQ(SEX,1),0,1) &CALC W2=%IF(%LT(POT,0),0,W2) &WEI W2 ----- CURRENT DISPLAY INHIBITED &FIT &DIS EM CYCLE DEVIANCE DF 1 896.9 38 ESTIMATE S.E. PARAMETER 1 144.8 0.7780 %GM SCALE PARAMETER TAKEN AS 23.60 Y-VARIATE SOD ERROR NORMAL LINK IDENTITY WEIGHT W2 LINEAR PREDICTOR %GM &FIT POT &DIS E CYCLE DEVIANCE DF 1 640.6 37 ESTIMATE S.E. PARAMETER 1 121.7 6.035 %GM 2 6.543 1.701 POT SCALE PARAMETER TAKEN AS 17.31 &FIT GP &DIS E CYCLE DEVIANCE DF 1 710.5 35 ESTIMATE S.E. PARAMETER 1 145.6 1.502 %GM 2 -4.164 2.070 GP(2) 3 -0.9544 2.070 GP(3) 4 1.796 2.070 GP(4) SCALE PARAMETER TAKEN AS 20.30 &FIT DOSE &DIS E CYCLE DEVIANCE DF 1 800.8 37 ESTIMATE S.E. PARAMETER 1 143.6 0.9449 %GM 2 0.1542 0.7314E-01 DOSE SCALE PARAMETER TAKEN AS 21.64 &FIT POT+GP &DIS E CYCLE DEVIANCE DF 1 584.6 34 ESTIMATE S.E. PARAMETER 1 127.5 6.844 %GM

ROELEE 3.1 281

2 5.114 1.890 POT 3 -2.831 1.968 GP(2) 4 -0.7567 1.907 GP(3) 5 0.6586 1.951 GP(4) SCALE PARAMETER TAKEN AS 17.19 &FIT POT*GP &DIS E CYCLE DEVIANCE DF 1 466.5 31 ESTIMATE S.E. PARAMETER 1 153.6 22.07 %GM 2 -2.254 6.213 POT 3 -44.11 24.30 GP(2) 4 -33.87 24.42 GP(3) 5 1.376 26.11 GP(4) 6 11.98 6.932 POT.GP(2) 7 9.358 6.881 POT.GP(3) 8 0.2444 7.223 POT.GP(4) SCALE PARAMETER TAKEN AS 15.05 &FIT POT+DOSE &DIS E CYCLE DEVIANCE DF 1 622.8 36 ESTIMATE S.E. PARAMETER 1 123.5 6.297 %GM 2 5.862 1.828 POT 3 0.7132E-01 0.7030E-01 DOSE SCALE PARAMETER TAKEN AS 17.30 &CALC W3=%IF(%LT(POT,0),0,1) &WEI W3 ----- CURRENT DISPLAY INHIBITED &FIT &DIS EM CYCLE DEVIANCE DF 1 1547. 78 ESTIMATE S.E. PARAMETER 1 145.3 0.5011 %GM SCALE PARAMETER TAKEN AS 19.84 Y-VARIATE SOD ERROR NORMAL LINK IDENTITY WEIGHT W3 LINEAR PREDICTOR %GM &FIT POT &DIS E CYCLE DEVIANCE DF 1 1286. 77 ESTIMATE S.E. PARAMETER 1 126.7 4.731 %GM 2 5.185 1.311 POT SCALE PARAMETER TAKEN AS 16.70 &FIT GP &DIS E CYCLE DEVIANCE DF 1 1325. 75 ESTIMATE S.E. PARAMETER 1 147.9 0.9644 %GM 2 -4.737 1.347 GP(2) 3 -2.857 1.347 GP(3) 4 -2.792 1.347 GP(4) SCALE PARAMETER TAKEN AS 17.67 &FIT DOSE &DIS E CYCLE DEVIANCE DF 1 1545. 77 ESTIMATE S.E. PARAMETER 1 145.5 0.6367 %GM 2 -0.1794E-01 0.4960E-01 DOSE

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SCALE PARAMETER TAKEN AS 20.06 &FIT POT+GP &DIS E CYCLE DEVIANCE DF 1 1115. 74 ESTIMATE S.E. PARAMETER 1 130.6 4.735 %GM 2 4.808 1.289 POT 3 -3.930 1.262 GP(2) 4 -3.023 1.245 GP(3) 5 -3.086 1.246 GP(4) SCALE PARAMETER TAKEN AS 15.07 &FIT POT*GP &DIS E CYCLE DEVIANCE DF 1 1012. 71 ESTIMATE S.E. PARAMETER 1 153.3 12.15 %GM 2 -1.486 3.357 POT 3 -41.38 14.88 GP(2) 4 -28.51 14.37 GP(3) 5 -18.62 15.29 GP(4) 6 10.58 4.176 POT.GP(2) 7 7.052 3.956 POT.GP(3) 8 4.338 4.197 POT.GP(4) SCALE PARAMETER TAKEN AS 14.26 &FIT POT+DOSE &DIS E CYCLE DEVIANCE DF 1 1269. 76 ESTIMATE S.E. PARAMETER 1 126.3 4.744 %GM 2 5.383 1.326 POT 3 -0.4565E-01 0.4577E-01 DOSE SCALE PARAMETER TAKEN AS 16.70 &FIT SEX &DIS E CYCLE DEVIANCE DF 1 1526. 77 ESTIMATE S.E. PARAMETER 1 145.8 0.7039 %GM 2 -1.038 1.002 SEX(2) SCALE PARAMETER TAKEN AS 19.82 &FIT SEX+POT &DIS E CYCLE DEVIANCE DF 1 1283. 76 ESTIMATE S.E. PARAMETER 1 127.3 4.940 %GM 2 -0.3929 0.9401 SEX(2) 3 5.084 1.340 POT SCALE PARAMETER TAKEN AS 16.88 &FIT SEX+POT+GP &DIS E CYCLE DEVIANCE DF 1 1113. 73 ESTIMATE S.E. PARAMETER 1 131.1 4.939 %GM 2 -0.3768 0.8945 SEX(2) 3 4.704 1.319 POT 4 -3.937 1.270 GP(2) 5 -3.010 1.252 GP(3) 6 -3.070 1.254 GP(4) SCALE PARAMETER TAKEN AS 15.24 &FIT SEX*GP &DIS E CYCLE DEVIANCE DF 1 1067. 71 ESTIMATE S.E. PARAMETER

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1 150.0 1.226 %GM 2 -4.376 1.781 SEX(2) 3 -5.080 1.734 GP(2) 4 -4.530 1.734 GP(3) 5 -7.150 1.734 GP(4) 6 0.9156 2.486 SEX(2).GP(2) 7 3.576 2.486 SEX(2).GP(3) 8 8.946 2.486 SEX(2).GP(4) SCALE PARAMETER TAKEN AS 15.03 &FIT SEX*GP +POT*GP &DIS E CYCLE DEVIANCE DF 1 815.4 67 ESTIMATE S.E. PARAMETER 1 163.3 11.74 %GM 2 -4.809 1.647 SEX(2) 3 -49.16 15.00 GP(2) 4 -40.17 14.12 GP(3) 5 -23.80 14.65 GP(4) 6 -3.634 3.187 POT 7 4.009 2.407 SEX(2).GP(2) 8 5.615 2.337 SEX(2).GP(3) 9 9.196 2.319 SEX(2).GP(4) 10 12.18 4.101 GP(2).POT 11 9.537 3.792 GP(3).POT 12 4.564 4.010 GP(4).POT SCALE PARAMETER TAKEN AS 12.17 &STOP __________________________________________________________________

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Appendix 8A Command File TOWKW.CMD

+ *** + *** Command File TOWKW.CMD + *** Used to test DATATOX F1 Statistics + *** Swith between Parametric and Non-parametric Statistics - + *** Test on ONEWAY variance first + SET PRINTER Y SET ALPHA Y SET SCREEN 132 SET TOTALS Y SET GLOSS 2 CLEAR CUTS FOR SEX 1 SELECT SET SEX 0 +SET BATCH 2 .SET FOOT $53 Footers on output $53 $53 1 : : $53 2 : : $53 3 : : $53 4 : : $53 5 : : $53 6 : : $53 SET TUMOURS 0 SET MULTI 0 SET METAST 0 SET FACTOR GROUP .SET lay $35 Text layout options $35 $35 1) Paper width: 132 $35 2) Paper length: 74 $35 3) Window top margin: 0 $35 4) Window bottom margin: 0 $35 5) Window left margin: 3 $35 6) Window right margin: 0 $35 7) First Page number: (0 for none) 1 $35 8) Page number: 1)Top or 2)Bottom 1 $35 9) Page number: 0)Invisible 1)Right 2)Centre or 3)Left 2 $35 10) Table number of next output: (0 for none) 1 $35 11) Number of animals or sections output per page: 0 $35 12) Minimum lines for new animal or section: 20 $35 13) Number of lines between animals or sections: 1 $35 14) Minimum lines for new organ or subsection: 20 $35 15) Number of lines between organs or subsections: 1 $35 16) First column for observations: 25 $35 17) Number of columns between groups: 3 $35 .SET HEAD $36 Headings on output $36 $36 1 :C:Appendix 8B - Table $36 2 :L: $36 3 :CUINSTEM DATATOX F1 Testing by Dr. J.S. Fry $36 4 :C: $36 5 :C: $36 6 :COMales $36 7 :L:@FIELD $36 8 :L: $36 9 :L: $36 $36 further heading for individual animal reports $36 10:L:Animal Tissue Observation $36 $36 further heading for group comparison analyses $36 11:L: $36 12:L: $36 13:L: Control 1 ppm 5 ppm 25 ppm

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$36 14TB: T T T T $36 .SET HEAD $136 22: OSodium SET dec 6 SET PARTITION 0 SET STRATA 0 SET CUT SODIUM 146 .SET TREND $1 Include Trend statistic ? Y $1 Contr Low Middl High $1 0 1 5 25 $1 .SET PROB $17 Probability options $17 $17 1) Probabilities: 1)actual p value 2)P<.01 3)*** 1 $17 2) Tails: 1)Two Tailed 2)One Tail (+ve) 3) One Tail (-ve) 1 $17 3) Filter results on Probs: 0) None or required level: 0 $17 4) Number of Probability levels: 4 $17 1 2 3 4 $17 (*) * ** *** $17 .1 .05 .01 .001 $17 .SET CONT $18 Position of control group: 1 $18 Contr Low Middl High $18 0 0 0 0 $18 + *** MALES ONLY - LEVENE TEST OF VARIANCE +PT FOR SEX 1 .SET HEAD $136 6 :COMales $136 7 :COLevene Test for Variance .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? N $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? n $12 16) Number of contrasts: 0 $12 + *** SET PRINTER N - for testing show Levene results &ONEWAY SODIUM + *** SET PRINTER Y IF ((BTOTAL < 0.05)^ (BTOTAL > 0.0)) + *** SIGNIFICANT VARIANCE **** + *** SWITCH TO NON-PARAMETRIC .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0

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$13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 &KWALLIS SODIUM ELSE + *** STAY AS PARAMETRIC .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 &ONEWAY ENDIF + *** REPEAT ABOVE TESTS FOR FEMALES FOR SEX 2 .SET HEAD $136 6 :COFemales .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? N $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 + *** SET PRINTER N &ONEWAY SODIUM + *** SET PRINTER Y IF ((BTOTAL < 0.05)^ (BTOTAL > 0.0)) + *** SIGNIFICANT VARIANCE **** + *** SWITCH TO NON-PARAMETRIC .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0

ROELEE 3.1 287

$13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 &KWALLIS SODIUM ELSE + *** STAY AS PARAMETRIC .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 12) Relative Group Mean difference ? Y $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 &ONEWAY ENDIF + *** repeat for ALL FOR .SET HEAD $136 6 :COMales and Females .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 2 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? N $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 + *** SET PRINTER N &ONEWAY SODIUM + *** SET PRINTER Y IF ((BTOTAL < 0.05)^ (BTOTAL > 0.0)) + *** SIGNIFICANT VARIANCE **** + *** SWITCH TO NON-PARAMETRIC .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0

ROELEE 3.1 288

$13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 &KWALLIS SODIUM ELSE + *** STAY AS PARAMETRIC .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 &ONEWAY ENDIF + *** REPEAT ABOVE USING Bartlett test for Variance .+PT FOR SEX 1 .SET HEAD $136 6 :COMales $136 7 :COBartlett Test for Variance .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? N $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 + *** SET PRINTER N &ONEWAY SODIUM + *** SET PRINTER Y IF ((BTOTAL < 0.05)^ (BTOTAL > 0.0)) + *** SIGNIFICANT VARIANCE **** + *** SWITCH TO NON-PARAMETRIC .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y

ROELEE 3.1 289

$13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 &KWALLIS SODIUM ELSE + *** STAY AS PARAMETRIC .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 &ONEWAY ENDIF + *** REPEAT ABOVE TESTS FOR FEMALES FOR SEX 2 .SET HEAD $136 6 :COFemales .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? N $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 + *** SET PRINTER N &ONEWAY SODIUM + *** SET PRINTER Y IF ((BTOTAL < 0.05)^ (BTOTAL > 0.0)) + *** SIGNIFICANT VARIANCE **** + *** SWITCH TO NON-PARAMETRIC .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0

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$13 11) Show totals over partitions ? Y $13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 &KWALLIS SODIUM ELSE + *** STAY AS PARAMETRIC .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 &ONEWAY ENDIF + *** repeat for ALL FOR .SET HEAD $136 6 :COMales and Females .SET one $12 One-way options $12 $12 1) Number of animals ? N $12 2) Mean Values ? N $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? n $12 5) St.Deviations ? n $12 6) Test variances: 0)No 1)Bartlett 2)Levene 1 $12 7) F statistic ? N $12 8) Print probabilities ? N $12 9) Geometric Mean Values ? n $12 10) Harmonic Mean Values ? n $12 11) Coefficient of variation ? n $12 12) Relative Group Mean difference ? N $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb0 $12 15) Degrees of freedom ? N $12 16) Number of contrasts: 0 $12 + *** SET PRINTER N &ONEWAY SODIUM + *** SET PRINTER Y IF ((BTOTAL < 0.05)^ (BTOTAL > 0.0)) + *** SIGNIFICANT VARIANCE **** + *** SWITCH TO NON-PARAMETRIC .SET KW $13 Kruskal-Wallis/Fry-Lee options $13 $13 1) Number of animals ? Y $13 2) Mean Ranks ? Y $13 3) Median Values ? Y $13 4) Confidence levels for Medians (give prob level): 0 $13 5) Range (Minimum,Maximum) ? Y $13 6) Kruskal-Wallis statistic ? Y $13 7) Print probabilities ? Y $13 8) Print exact probabilities for comparisons ? Y $13 9) Yates correction ? Y $13 10) Minimum total outside one rank: 0 $13 11) Show totals over partitions ? Y

ROELEE 3.1 291

$13 12) Quantiles ? Y $13 13) Quantile range ? Y $13 14) Trend Test 1)RoeLee 2)Jonckeere 2 $13 15) Adjust Ps 0)No 1)Steel 2)Bonf 3)Holm 4)Hommel 5)Hochb 1 $13 16) Missing Values ? Y $13 &KWALLIS SODIUM ELSE + *** STAY AS PARAMETRIC .SET oneway $12 One-way options $12 $12 1) Number of animals ? Y $12 2) Mean Values ? Y $12 3) Confidence levels for Means (give prob level): 0 $12 4) St.Errors ? Y $12 5) St.Deviations ? Y $12 6) Test variances: 0)No 1)Bartlett 2)Levene 0 $12 7) F statistic ? Y $12 8) Print probabilities ? Y $12 9) Geometric Mean Values ? Y $12 10) Harmonic Mean Values ? Y $12 11) Coefficient of variation ? Y $12 12) Relative Group Mean difference ? Y $12 13) T-test 1)RoeLee 2)2 group 3)Welch 4)Pitman 1 $12 14) Adjust Ps 0)No 1)Dunnett 2)Bonf 3)Holm 4)Hommel 5)Hochb1 $12 15) Degrees of freedom ? Y $12 16) Number of contrasts: 0 $12 &ONEWAY ENDIF WRITE ITOWKW __________________________________________________________________

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Appendix 8B Results from TOWKW.CMD

1 Appendix 8B - Table 1 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males Levene Test for Variance Control 1 ppm 5 ppm 25 ppm Total Trend Lev P 0.165494 0.137782 0.879784 0.256734 N 10 10 10 10 40 Mean 150.020000 144.940000 145.490000 142.870000 145.830000 GMean 150.010972 144.895886 145.443061 142.845482 145.775537 HMean 150.001988 144.851332 145.395380 142.820376 145.720509 St.Err 0.549909 1.186142 1.222152 0.871914 0.634956 St.Dev 1.738965 3.750911 3.864784 2.757233 4.015815 CoefV 1.159156 2.587906 2.656392 1.929889 2.753765 %dev -3.386215 -3.019597 -4.766031 F 13.022939 10.355665 25.798452 9.159348 14.413788 df 36 36 36 36 36 P 0.000928 0.002731 0.000012 0.000122 0.000543 Dun P 0.002621 0.007566 0.000035 Females Lev P 0.191224 0.000087 0.062374 0.002818 Kruskal-Wallis Analysis Jonckheere S = 172 N 9 10 10 10 39 MRank 18.222222 11.200000 23.150000 27.250000 20.000000 Median 145.300000 142.200000 147.600000 147.850000 145.800000 Min 144.000000 127.400000 132.100000 144.400000 127.400000 Max 147.400000 147.900000 150.200000 149.700000 150.200000 Miss 1 0 0 0 1 Q1 144.000000 127.400000 132.100000 144.400000 127.400000 Q5 144.000000 127.400000 132.100000 144.400000 132.100000 Q25 145.100000 140.900000 142.200000 145.800000 142.900000 Q75 146.300000 145.400000 148.900000 149.300000 148.100000 Q95 147.400000 147.900000 150.200000 149.700000 149.700000 Q99 147.400000 147.900000 150.200000 149.700000 150.200000 QRange 1.200000 4.500000 6.700000 3.500000 5.200000 ChiSq 3.843371 1.218206 4.689895 10.986713 4.778741 P 0.049943 0.269713 0.030341 0.011798 0.031350 Stl P 0.125311 0.551486 0.078608 ExP 0.050553 1.000000 0.029293 One Way Analysis of Variance Males and Females Lev P 0.186617 0.040225 0.955180 0.114956 N 19 20 20 20 79 Mean 147.947368 143.210000 145.090000 145.155000 145.317722 GMean 147.924613 143.122827 144.999076 145.119264 145.248211 HMean 147.901941 143.032301 144.905224 145.082993 145.176440 St.Err 0.612700 1.125468 1.159739 0.733610 0.501076 St.Dev 2.670699 5.033247 5.186511 3.280801 4.453658 CoefV 1.805168 3.514592 3.574685 2.260206 3.064773 %dev -3.202063 -1.931341 -1.887407 F 12.374555 4.501816 4.299329 4.183898 0.148515 df 75 75 75 75 75 P 0.000743 0.037162 0.041562 0.008558 0.701050 Dun P 0.002121 0.093766 0.104125

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2 Appendix 8B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ One Way Analysis of Variance Males Bartlett Test for Variance Control 1 ppm 5 ppm 25 ppm Total Trend Var P 0.031708 0.026099 0.185860 0.114570 N 10 10 10 10 40 Mean 150.020000 144.940000 145.490000 142.870000 145.830000 GMean 150.010972 144.895886 145.443061 142.845482 145.775537 HMean 150.001988 144.851332 145.395380 142.820376 145.720509 St.Err 0.549909 1.186142 1.222152 0.871914 0.634956 St.Dev 1.738965 3.750911 3.864784 2.757233 4.015815 CoefV 1.159156 2.587906 2.656392 1.929889 2.753765 %dev -3.386215 -3.019597 -4.766031 F 13.022939 10.355665 25.798452 9.159348 14.413788 df 36 36 36 36 36 P 0.000928 0.002731 0.000012 0.000122 0.000543 Dun P 0.002621 0.007566 0.000035 Females Var P 0.000127 0.000052 0.179023 0.000011 Kruskal-Wallis Analysis N 9 10 10 10 39 MRank 18.222222 11.200000 23.150000 27.250000 20.000000 Median 145.300000 142.200000 147.600000 147.850000 145.800000 Min 144.000000 127.400000 132.100000 144.400000 127.400000 Max 147.400000 147.900000 150.200000 149.700000 150.200000 Miss 1 0 0 0 1 Q1 144.000000 127.400000 132.100000 144.400000 127.400000 Q5 144.000000 127.400000 132.100000 144.400000 132.100000 Q25 145.100000 140.900000 142.200000 145.800000 142.900000 Q75 146.300000 145.400000 148.900000 149.300000 148.100000 Q95 147.400000 147.900000 150.200000 149.700000 149.700000 Q99 147.400000 147.900000 150.200000 149.700000 150.200000 QRange 1.200000 4.500000 6.700000 3.500000 5.200000 ChiSq 3.843371 1.218206 4.689895 10.986713 4.778741 P 0.049943 0.269713 0.030341 0.011798 0.031350 Stl P 0.125311 0.551486 0.078608 ExP 0.050553 1.000000 0.029293 One Way Analysis of Variance Males and Females Var P 0.009625 0.006857 0.387617 0.013558

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3 Appendix 8B - Table 2 INSTEM DATATOX F1 Testing by Dr. J.S. Fry _________________________________________ Kruskal-Wallis Analysis Males and Females Bartlett Test for Variance Control 1 ppm 5 ppm 25 ppm Total Trend Jonckheere S = -360 N 19 20 20 20 79 MRank 53.815789 28.450000 42.325000 36.100000 40.000000 Median 148.100000 143.950000 146.900000 145.250000 145.800000 Min 144.000000 127.400000 132.100000 135.700000 127.400000 Max 153.200000 150.900000 150.200000 149.700000 153.200000 Miss 1 0 0 0 1 Q1 144.000000 127.400000 132.100000 135.700000 127.400000 Q5 144.000000 132.450000 133.250000 138.750000 135.700000 Q25 145.300000 141.200000 143.350000 143.600000 143.600000 Q75 150.000000 146.500000 148.500000 147.850000 148.300000 Q95 153.200000 149.400000 150.050000 149.550000 150.600000 Q99 153.200000 150.900000 150.200000 149.700000 153.200000 QRange 4.700000 5.300000 5.150000 4.250000 4.700000 ChiSq 10.808199 2.137549 6.905970 12.739165 2.491403 P 0.001011 0.143731 0.008591 0.005236 0.116137 Stl P 0.002911 0.326061 0.023548 ExP

Documents

Test of Statistics 6 RoeLee 3.1 Author: John S Fry Date: … · 2018. 4. 5. · 6.1 descriptive statistics 6.2 2-group t-test 6.3 welch test 6.4 fisher-pitman test 6.5 dunnett test