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STATISTICAL ANALYSIS USING SAS/PC -_---__----__-__----------------- ................................. EXA9PLE OUTPUT LISTIXGS ___-___---------------- ....................... Prepared by: W. Bergerud Biometries Section Research Branch Ministry of Forests 634.90971 1 BCMF RES

# STATISTICAL ANALYSIS USING SAS/PC ... · example ---- for sas/pc practice program sec222 ---- descriptive statistics--using proc univariate univariate procedure frequency table value

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STATISTICAL ANALYSIS USING SAS/PC - _ - - - _ _ - - - - _ _ - _ _ - - - - - - - - - - - - - - - - - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

EXA9PLE OUTPUT LISTIXGS _ _ _ - _ _ _ - - - - - - - - - - - - - - - - . . . . . . . . . . . . . . . . . . . . . . .

P r e p a r e d b y : W . B e r g e r u d B i o m e t r i e s S e c t i o n R e s e a r c h B r a n c h M i n i s t r y of F o r e s t s

634.90971 1 BCMF RES

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC211 ---- DESCRIPTIVE STATISTICS

................................

N Obs Variable N Minimum Maximum Mean Std Dev ............................................................................

32 Y 32 6.2837067 31.1259953 19.9066500 6.6882840

X1 32 0 30.0000000 15.0000000 9.3670665

X2 32 51.2983036 91.1108736 70.7628355 11.4173402

X3 32 6.0343705 8.9434137 7.3167244 0.7947923

N Obs Variable N Minimum Max imum Mean Std Dev ............................................................................

32 Y 32 8.5027750 33.1766276 20.9146707 6.7409455 X1 32 0 30.0000000 15.0000000 9.3670665 X2 32 51.4915382 90.6308617 70.9133834 11.7384693 X 3 32 6.0634582 8.9933708 7 5933071 0.8466239 ............................................................................

N Obs Variable N Minimum Max imum Mean Std Dev

N Obs Variable N Minimum Max imum Mean Std Dev ............................................................................ 32 Y 32 11.1290774 37.1589973 23.6263785 7.6234458

X1 32 0 30.0000000 15.0000000 9.3670665 X2 32 51.3540611 88.5683248 70.7562759 11.7308714 X3 32 6.1089413 8.9610628 7.5690351 0.9280913 ............................................................................

N Obs Variable N Minimum Maximum Mean Std Dev ............................................................................ 32 Y 32 11.5802065 37.7946858 24.6326588 7.3383401

X1 32 0 30.0000000 15.0000000 9.3670665 X2 32 52.3599988 91.2374935 70.7277767 11.0746768 X3 32 6.1129342 8.6472279 7.4030247 0.6701942 ............................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC211 ---- DESCRIPTIVE STATISTICS

N Obs Variable N Minimum Max imum Mean Std Dev ............................................................................ 32 Y 32 13.0543168 40.6361627 25.4910944 7.6446174

X1 32 0 30.0000000 15.0000000 9.3670665 X2 32 51.6775232 92.2882891 70.8459353 11.7734538 X3 32 6.0064078 8.9465957 ' 7.3640413 0.8809703 ............................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC211 ---- DESCRIPTIVE STATISTICS

N Obs Variable N Minimum Maximum Mean Std Dev

N Obs Variable N Minimum Maximum Mean Std Dev ............................................................................ 96 Y 96 11.1290774 40.6361627 24.5833772 7.4962514

X1 96 0 30.0000000 15.0000000 9.2679413 X2 96 51.3540611 92.2882891 70.7766626 11.4088608 X3 96 6.0064078 8.9610628 7.4453670 0.8299887 ............................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC2ll ---- DESCRIPTIVE STATISTICS

N Obs Variable N Minimum Max imum Mean Std Dev

N Obs Variable N Minimum Max imum Mean Std Dev

N Obs Variable N Minimum Max imum Mean Std Dev ............................................................................ 64 Y 64 8.4315634 40.6361627 23.4970388 7.5123738

X1 64 0 30.0000000 15.0000000 9.2924274 X2 64 51.6775232 92.2882891 70.8314499 11.5026169 X3 64 6.0064078 8.9465957 7.5448747 0.9058737 ............................................................................

A B NUM MEANY

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC212 ---- LISTING OF MEANS FOR Y

STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC212 ---- LISTING OF MEANS FOR Y

A NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC212 ---- LISTING OF MEANS FOR Y

B NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Moments

N Mean Std Dev Skewness

2 USS cv T:Mean=O

1 " Sgn Rank -2.. N-urn-.^.= 0

r,

100% Max 75% 43 50% Med 25% Q1

0% Min

Range 43-Q1 Mode

32 Sum Wgts 32 19.90665 Sum 637.0128 6.688284 Variance 44.73314 -0.11125 Kurtosis -0.69778 14067.52 CSS 1386.727 33.59824 Std Mean 1 16.83676 Prob>:TI

264 Prob>lSI - --_.._ 32 0 .9 6 53-01- FraMw---- "l

--

Quantiles(Def=5)

Extremes

Lowest Obs Highest Obs 6.283707 ( 1) 28.52644( 29 ) 7.769477( 2) 28.89917( 31 ) 9 343431 ( 3) 30.03199( 28 12.41474 ( 5) 30.05756( 30) 12.90661 ( 6) 31.126( 32 )

EXAMPLE FOR SAS/PC PRACTICE -2, ---- PROGRAM SEC222 ----

DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Stem Leaf # 30 011 3 28 59 2 26 05 2 24 37 2 22 16667 5 20 9 1 18 12 2 16 2678849 7 14 19 2 12 497' ,, : 11.45 1 2 . q , 1-5. f 3 10

Boxplot I I I

Normal Probability Plot *

,L;&

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Frequency Table

Value Count 6.283707 1 7.769477 1 9.343431 1 12.41474 1 12.90661 1 13.71387 1 14.12113 1 15.87666 1 16.24995 1 16.60208 1 16.74328 1 16.7607 1

16.81456 1 17.3694 1

17.92136 1 19.14101 1

Percents Cell Cum 3.1 3.1 3.1 6.2 3.1 9.4 3.1 12.5 3.1 15.6 3.1 18.8 3.1 21.9 3.1 25.0 3.1 28.1 3.1 31.3 3.1 34.4 3.1 37.5 3.1 40.6 3.1 43.7 3.1 46.9 3.1 50.0

Value Count 19.20613 1 21.86394 1 22.07582 1 22.57999 1 22.6186 1 22.64204 1 22.74785 1 25.33618 1 25.73185 1 26.03986 1 27.49743 1 28.52644 1 28.89917 1 30,03199 1 30.05756 1

31.126 1

Percents Cell Cum 3.1 53.1 3.1 56.2 3.1 59.4 3.1 62.5 3.1 65.6 3.1 68.7 3-1 71.9 3.1 75.0 3.1 78.1 3.1 81.2 3.1 84.4 3.1 87.5 3.1 90.6 3.1 93.7 3.1 96.9 3.1 100.0

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Moments

N Mean Std Dev Skewness uss cv T:Mean=O Sgn Rank Num ^ = 0 W:Normal

Sum Wgts Sum Variance Kurtosis css Std Mean Prob> :TI Prob> l S I

100% Max 33.17663 99% 33.17663 75% 43 25.86753 95% 32.38452 50% Med 20.03327 90% 30.64345 25% Q1 15.85753 10% 11.94849 0% Min 8.502775 5% 10.38758

1% 8.502775 Range 24.67385 Q3-Q1 10.01001 Mode 8.502775

Extremes

Lowest Obs Highest Obs 8.502775 ( 1) 28.60686( 27 10.38758( 2) 30.64345( 29) 11.64312 ( 3) 32.21362( 30 11.94849 ( 4) 32.38452( 32 12.29334( 5) 33.17663( 31

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Variable=Y

Stem Leaf 32 242 30 6 28 16 26 16 24 656 22 0 20 01457 18 6027 16 488 14 213 12 3 10 469 8 5

- - - -+- - - -+- - - -+- - - -+

Boxplot

Normal Probability Plot * * + + + *

* + + + * * + +

* * + + * * * +

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Frequency Table

Value Count 8.502775 1 10 38758 1 11.64312 1 11.94849 1 12.29334 1 14.23835 1 15.07108 1 15.29011 1 16.42495 1 17.79086 1 17.81351 1 18.63011 1 18.9521 1 19.1827 1

19.68585 1 19.96847 1

Percents Cell Cum 3.1 3.1 3.1 6.2 3.1 9.4 3.1 12.5 3.1 15.6 3.1 18.8 3.1 21.9 3.1 25.0 3.1 28.1 3.1 31.3 3.1 34.4 3.1 37.5 3.1 40.6 3.1 43.7 3.1 46.9 3.1 50.0

Value Count 20.09807 1 21.44013 1 21.50152 1 21.69345 1 23.0267 1 24.64309 1 25.52992 1 25.64192 1 26.09315 1 26.63489 1 28.11816 1 28.60686 1 30.64345 1 32.21362 1 32.38452 1 33.17663 1

Percents Cell Cum 3.1 ' 53.1 3.1 56.2 3.1 59.4 3.1 62.5 3.1 65.6 3.1 68.7 3.1 71.9 3.1 75.0 3.1 78.1 3.1 81.2 3.1 84.4 3.1 87.5 3.1 90.6 3.1 93.7 3.1 96.9 3.1 100.0

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Moments

N Mean Std Dev Skewness USS cv T:Mean=O Sgn Rank Num * = 0 W:Normal

Sum Wgts Sum Variance Kurtosis CSS Std Mean Prob> !TI Prob> l S I

100% Max 34.22621 99% 34.22621 75% 43 26.45838 95% 32.39177 50% Med 21.41949 90% 30.23064 25% Q1 16.37685 10% 12.47368 0% Min 8.431563 5% 9.083568

1% 8.431563 Range 25.79464 43-41 10.08153 Mode 8.431563

Extremes

Lowest Obs Highest Obs 8.431563( 2) 29.07286( 26 9.083568( 1) 30.23064( 29 11.21188 ( 3) 31.04452( 32) 12.47368 ( 4) 32.39177( 30) 12.94893 ( 6) 34.22621( 31

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

.................................. A=l B=5 ...................................

UNIVARIATE PROCEDURE

Stem Leaf 34 2 32 4 30 20 28 991 26 6 24 05333 22 2 20 92358 18 7007 16 16 14 9 12 592 10 2 8 41

- - - - + - - - - + - - - - + - - - - +

Boxplot I I

Normal Probability Plot + + *

* + + * + * +

* * + * +

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Frequency Table

Percents Value Count Cell Cum

8.431563 1 3.1 3.1 9.083568 1 3.1 6.2 11.21188 1 3.1 9.4 12.47368 1 3.1 12.5 12.94893 1 3.1 15.6 13.16898 1 3.1 18.8 14.9113 1 3.1 21.9

16.14443 1 3.1 25.0 16.60926 1 3.1 28.1 18.73292 1 3.1 31.3 18.9801 1 3.1 34.4

19.00059 1 3.1 37.5 19.68085 1 3.1 40.6 20.88374 1 3.1 43.7 21 .I923 1 3.1 46.9

21.29269 1 3.1 50.0

Value Count 21.5463 1 21.7671 1

23.22816 1 23.95711 1 24.49637 1 25.29555 1 25.31961 1 25.32045 1 27.59631 1 28.90913 1 28.94659 1 29.07286 1 30.23064 1 31.04452 1 32.39177 1 34.22621 1

Percents Cell Cum 3.1 53.1 3.1 56.2 3.1 59.4 3.1 62.5 3.1 65.6 3.1 68.7 3.1 71.9 3.1 75.0 3.1 78.1 3.1 81.2 3.1 84.4 3.1 87.5 3.1 90.6 3.1 93.7 3.1 96.9 3.1 100.0

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Moments

N Mean Std Dev Skewness USS cv T:Mean=O Sgn Rank Num ^ = 0 W: Normal

Sum Wgts Sum Variance Kurtosis CSS Std Mean Prob> : T: Prob> lS I

100% Max 37.159 99% 37.159 75% 43 29.27307 95% 36.66851 50% Med 24.25401 90% 34.07397 25% Q1 17.24037 10% 11.98618 0% Min 11.12908 5% 11.39492

1% 11.12908 Range 26.02992 43-41 12.0327 Mode 11.12908

Extremes

Lowest Obs Highest Obs 11.12908( 4) 33.57798( 28) 11.39492 ( 3) 34.07397( 30 11.63437 ( 2) 34.37763( 29 11.98618 ( 1) 36.66851( 31 14.55797 ( 5) 37.159( 32

Stem Leaf # 3 77 2 3 011444 6 2 56666779 8 2 022333 6 1 556779 6 1 1122 4

----+----+----+----+

Multiply Stem.Leaf by 10**+1

Boxplot I 1

I 1

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Normal Probability Plot 37.5+ + * + + + + *

I I * * + * * + * I * * * * * * * * + I I * * * * * + I I I + + * * * * *

12.5+ * + * + * + * * +-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+

-2 -1 0 +1 +2

Frequency Table

Percents Value Count Cell Cum

11 .I2908 1 3.1 3.1 11.39492 1 3.1 6.2 11.63437 1 3.1 9.4 11.98618 1 3.1 12.5 14 55797 1 3.1 15.6 15.23399 1 3.1 18.8 16.13954 1 3.1 21.9 17.19177 1 3.1 25.0 17.28897 1 3.1 28.1 19.31358 1 3.1 31.3 20.16102 1 3.1 34.4 21.62686 1 3.1 37.5 21.64648 1 3.1 40.6 22.5492 1 3.1 43.7

23.13384 1 3.1 46.9 23.42514 1 3.1 50.0

Value 25.08289 25.53721 25.67436 25.78417 25.96556 26.56617 26.82444 28.70287 29.84328 30.60428 31.18889 33.57798 34.07397 34.37763 36.66851

37.159

Count 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Percents Cell Cum 3.1 53.1 3.1 56.2 3.1 59.4 3.1 62.5 3.1 65.6 3.1 68.7 3.1 71.9 3.1 75.0 3.1 78.1 3.1 81.2 3.1 84.4 3.1 87.5 3.1 90.6 3.1 93.7 3.1 96.9 3.1 100.0

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Moments

N Mean Std Dev Skewness USS cv T:Mean=O Sgn Rank Num ^ = 0 W:Normal

Sum Wgts Sum Variance Kurtosis CSS Std Mean Prob> lT I Prob> l S I

100% Max 37.79469 99% 37.79469 75% 43 29.84225 95% 36.00831 50% Med 24.57296 90% 34.23742 25% Q1 18.341 10% 14.43515 0% Min 11.58021 5% 13.77413

1% 11.58021 Range 26.21448 43-41 11.50125 Mode 11.58021

Extremes

Lowest Obs Highest Obs 11.58021 ( 1) 33.72587( 29 13.77413 ( 3) 34.23742( 28) 14.20899 ( 4) 34.69706( 30) 14.43515 ( 5) 36.00831( 31) 14.60358 ( 2) 37.79469( 32

Stem Leaf # 3 568 3 3 002344 6 2 55588889 8 2 022334 6 1 56779 5 1 2444 4

----+----+----+----+

Multiply Stem.Leaf by 10**+1

Boxplot I I

+-----+ *--+--* I I I I

+-----+

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Normal Probability Plot 37.5+ + * + + + + *

I I * * * + * * + * I I + * * * * * + I I + + * * * * * * I I + + + + * * * * *

12.5+ * + + + * + * * * +-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+-- - -+

-2 -1 0 +1 +2

Frequency Table

Value 11.58021 13.77413 14.20899 14.43515 14.60358 16.42796 17.16203 17.45137 19.23063 19.76653 21.72319 22.02874 22.83232 23.48779 24.31237 24.53097

Count 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Percents Cell Cum 3.1 3.1 3.1 6.2 3.1 9.4 3.1 12.5 3.1 15.6 3.1 18.8 3.1 21.9 3.1 25.0 3.1 28.1 3.1 31.3 3.1 34.4 3.1 37.5 3.1 40.6 3.1 43.7 3.1 46.9 3.1 50.0

Value Count 24.61495 1 24.74488 1 27.50636 1 27.50816 1 27.82586 1 28.35373 1 28.58297 1 29.6686 1 30.0159 1 32.07617 1 33.3282 1 33.72587 1 34.23742 1 34.69706 1 36.00831 1 37.79469 1

Percents Cell Cum 3.1 53.1 3.1 56.2 3.1 59.4 3.1 62.5 3.1 65.6 3.1 68.7 3.1 71.9 3.1 75.0 3.1 78.1 3.1 81.2 3.1 84.4 3.1 87.5 3.1 90.6 3.1 93.7 3.1 96.9 3.1 100.0

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Moments

N Mean Std Dev Skewness USS cv T:Mean=O Sgn Rank Num ^ = 0 W:Normal

100% Max 75% 43 50% Med 25% Q1 0% Min

Range 43-Q1 Mode

Sum Wgts Sum Variance Kurtosis CSS Std Mean Prob> I T I Prob> l S I

Extremes

Lowest Obs Highest Obs 13.05432 ( 1) 33.7531( 26 13.92382( 3) 35.05378( 28 14.5522( 2) 36.10716( 30)

14.63888 ( 5) 38.79855( 31 15.00925 ( 4) 40.63616( 32)

Stem Leaf # 4 1 1 3 569 3 3 011444 6 2 555667889 9 2 2334 4 1 5556799 7 1 34 2

- - - -+-- - -+-- - -+-- - -+

Multiply Stem.Leaf by 10**+1

Boxplot I I

I I

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE

Normal Probability Plot 42.5+ + + * + + + +

I I * + * + * + + I I * * * * + * +

27.5+ * * * * * * I I + + * * * * * * I I + + * + * * * *

12.5+ * + + + + * + * * +----+----+----+----+----+----+----+----+----+----+----+

-2 -1 0 +1 +2

Frequency Table

Value Count 13.05432 1 13.92382 1 14.5522 1

14.63888 1 15.00925 1 16.41136 1 17.48479 1 18.9952 1

19.31897 1 21.61943 1 22.51715 1 23 .I7216 1 23.76931 1 24.63169 1 24.63959 1 24.73108 1

Percents Cell Cum 3.1 3.1 3.1 6.2 3.1 9.4 3.1 12.5 3.1 15.6 3.1 18.8 3.1 21.9 3.1 25.0 3.1 28.1 3.1 31.3 3.1 34.4 3.1 37.5 3.1 40.6 3.1 43.7 3.1 46.9 3.1 50.0

Value Count 25.96002 1 26.15981 1 27.48238 1 27.88621 1 27.93652 1 28.55718 1 29.72224 1 30.87262 1 31.0914 1 33.60848 1 33.62022 1 33.7531 1

35.05378 1 36 .lo716 1 38.79855 1 40.63616 1

Percents Cell Cum 3.1 53.1 3.1 56.2 3.1 59.4 3.1 62.5 3.1 65.6 3.1 68.7 3.1 71.9 3.1 75.0 3.1 78.1 3.1 81.2 3.1 84.4 3.1 87.5 3.1 90.6 3.1 93.7 3.1 96.9 3.1 100.0

.EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE Schematic Plots

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

UNIVARIATE PROCEDURE Schematic Plots

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC222 ---- DESCRIPTIVE STATISTICS--USING PROC UNIVARIATE

A B NUM MEANY STD VAR MIN MAX MEDIAN IQD SKEWNESS

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- OUTPUT FROM PROC SUMMARY

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF GRAND MEAN FOR Y

OBS NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF A

NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF B

NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF C

NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF A AND B

A B NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF A AND C

A C NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF B AND C

B C NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC23 ---- LISTING OF MEAN FOR Y BY VALUES OF A, B, AND C

A B C NUM MEANY STD STDERR VAR CV MIN MAX

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y .......................................................................... I 1 I NUM I MEAN I STD 1STDERR 1 VAR I CV I MIN 1 MAX I

EXAMPLE FOR SAS/PC PRACTICE. ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X1 .......................................................................... I I I NUM 1 MEAN 1 STD 1STDERR 1 VAR I CV ! MIN I MAX I

:A I I I I I I I I 1 I I I I I I I I I

!----------I I I I I I I I I I I I I I 6 I I

I1 i 961 15.001 9.271 0.951 85.891 61.791 0.00: 30.001 I - - - - - - - - - -+- - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - - l 12 1 961 15.001 9.27: 0.951 85.891 61.791 0.001 30.001 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X2 .......................................................................... I I I NUM 1 MEAN I STD 1STDERR 1 VAR : CV I MIN 1 MAX :

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y .......................................................................... I 1 1 NUM 1 MEAN I STD 1STDERR I VAR I CV I MIN I MAX I ; - - - - - - - - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

1 B I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I

13 1 641 21.771 7.361 0.921 54.121 33.801 6.281 37.161 ( - - - - - - - - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

1 4 1 641 22.771 7.241 0.901 52.371 31.781 8.501 37.791 : ----------+-----+-------+-------+-------+-------+-------+-------+------- ;

: 5 1 641 23.501 7.511 0.941 56.44: 31.971 8.431 40.641 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X1 .......................................................................... I 1 I NUM I MEAN I STD 1STDERR I VAR I CV I MIN I M A X I

1 B I I I I I I I , I I I I I I I I I I

I I I I I I I I I I I I I I I I

1 3 1 641 15.001 9.291 1.161 86.35: 61.951 0.00i 30.001 ; - - - - - - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

14 1 641 15.001 9.291 1.161 86.351 61.95: 0.001 30.001

15 1 641 15.00; 9.291 1.161 86.351 61.951 0.00: 30.001 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X2 .......................................................................... I I I NUM 1 MEAN I STD lSTDERR I VAR I CV I MIN I MAX 1 ; ----------+-----+-------+-------+-------+-------+-------+-------+------- :

1 B I I I I I I I I I I I I I I I I I I

I----------; I 1 I I I I I I I I I I I I I I

: 3 1 641 70.761 11.481 1.441 131.861 16.231 51.301 91.111 ; ----------+-----+-------+-------+-------+-------+-------+-------+------- ; 14 1 641 70.821 11.321 1.421 128.161 15.991 51.491 91.241 ; ----------+-----+-------+-------+-------+-------+-------+-------+------- ;

15 1 641 70.831 11.501 1.441 132.311 16.241 51.681 92.291 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y .......................................................................... I 1 I NUM I MEAN 1 STD 1STDERR 1 VAR I CV I MIN I MAX 1 ; - - - - - - - - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

1 C I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I

12 1 961 17 .40 : 4.991 0.511 24.861 28.651 6.281 27.941

19 1 961 27.951 5.291 0.541 27.961 18.921 16.741 40.641 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE. ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X 1 .......................................................................... I I I NUM : MEAN 1 STD 1STDERR I VAR I CV 1 MIN I MAX :

I C I I I I I I I I I 1 I I I I I , I I

; - - - - - - - - - - : I I I I I I I I I I I I I I I I

12 1 961 15.001 9.271 0.951 85.891 61.791 0 . 0 0 : 30.001

19 1 961 15.001 9.271 0.951 85.891 61.791 0.001 30 .00 : ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X2 .......................................................................... I I I NUM 1 MEAN : STD ISTDERR 1 VAR I CV 1 MIN I M A X 1 ! - - - - - - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - l

1 C I I I I I I I I I I I I I I I I I I

I I I I I I I I I I 1 I I I I I

12 1 961 70.601 11.491 1.171 131.921 16 .27 : 51.351 90.861

: 9 1 961 71.001 11.321 1.161 128.181 15.941 51.30: 92.29: ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y

I I 1 NUM I MEAN 1 STD 1STDERR 1 VAR I CV I MIN I MAX I ; - - - - - - - - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

:A 1B I I I I I I I I I I I I I I I I I I

;----+-----I I I I I I I I I I I I I I I I I

11 13 1 321 19.911 6.691 1.181 44.731 33.601 6.281 31.131 I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; 1

I t 14 1 321 20.911 6.741 1.191 45.441 32.231 8.501 33.18: I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; 1

I I 15 1 321 21.501 6.931 1.231 48.041 32.231 8.431 34.231 ; - - - -+-- - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

12 13 1 321 23.631 7.621 1.351 58.121 32.271 11.131 37.161 I I

I 1 14 1 321 24.631 7.341 1.301 53.851 29.791 11.581 37.791 1 1

I I 15 1 321 25.491 7.641 1.351 58.441 29.991 13.051 40.641

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X1

I I 1 NUM 1 MEAN 1 STD ISTDERR 1 VAR 1 CV 1 MIN : MAX 1 ' - - - - - - - - - - + - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - 1 1A 1B I I I I I I I I I

I I I I I I I I I

; - - - - + - - - - - I I I I I I I I I I I I I I I I I

11 13 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001 I I

I I 14 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y

I t 1 NUM 1 MEAN 1 STD 1STDERR 1 VAR I CV I MIN I MAX 1 ; - - - - - - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

IA 1C I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I

11 12 1 481 16.011 4.791 0.691 22.971 29.941 6.281 25.641 I I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I I 1 9 1 481 25.541 4.761 0.691 22.631 18.621 16.741 34.231 ; - - - -+-- - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

12 12 1 481 18.801 4.831 0.701 23.281 25.661 11.131 27.94: I I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I I 19 1 481 30.361 4.691 0.681 22.031 15.461 21.721 40.641 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X1 .......................................................................... I I 1 NUM 1 MEAN 1 STD 1STDERR 1 VAR 1 CV 1 MIN : MAX : ; - - - - - - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

1A :C I I I I I I I I I I I I I I I I I I

I - - - - + - - - - - ' I I I I I I I I I I I I I I I I

11 12 1 481 15.001 9.321 1.341 86.811 62.111 0.001 30.001 I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I

I t 19 1 481 15.001 9.321 1.341 86.811 62.111 0.001 30.001

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X2 .......................................................................... I I 1 NUM 1 MEAN 1 STD 1STDERR 1 VAR 1 CV 1 MIN 1 MAX I ;----------+-----+-------+-------+-------+-------+-------+-------+-------;

1A 1C I I I I I I I I I I I I I 1 I I I I

:----+-----I I I I I I I I I I I I I I I I I

11 12 1 481 70.751 11.501 1.661 132.321 16.261 51.491 90.631 I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I I 1 19 1 481 70.911 11.421 1.651 130.471 16.111 51.301 91.111

12 12 1 481 70.461 11.591 1.671 134.291 16.451 51.351 90.861 I I

I 1 19 1 481 71.101 11.341 1.641 128.591 15.951 51.491 92.291 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y .......................................................................... I I 1 NUM 1 MEAN 1 STD 1STDERR 1 VAR I CV I MIN I MAX I ; - - - - - - - - - -+- - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - - ;

1B 1C I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I

13 12 1 321 16.431 4.901 0.871 24.021 29.831 6.281 25.781 I I :-----+-----+-------+-------+-------+-------+-------+-------+-------; I I 19 1 321 27.101 5.211 0.921 27.161 19.231 16.741 37.161 : - - - -+-- - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

14 12 1 321 17.631 4.851 0.861 23.541 27.511 8.501 27.511 I I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I I 19 1 321 27.911 5.321 0.941 28.331 19.071 17.791 37.791

15 12 1 321 18.151 5.201 0.921 27.011 28.631 8.431 27.941 1 I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I 1 1 9 1 321 28.841 5.351 0.951 28.641 18.551 18.981 40.641

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE X1

I I 1 NUM 1 MEAN 1 STD 1STDERR I VAR I CV I MIN : MAX 1 ; - - - - - - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

1B 1C I I I I I I I I I I I I I I I I I I

I----+-----' I I I I I I I I I I I I I I I I

13 12 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001 I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I

I 1 19 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001 ; - - - -+ - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

14 12 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001 I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; I

I I 19 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001 : - - - -+- - - - -+- - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - - ;

15 12 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.001 I I ;-----+-----+-------+-------+-------+-------+-------+-------+-------; 1 1 1 9 1 321 15.001 9.371 1.661 87.741 62.451 0.001 30.00:

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC24 ---- TABLE OF DESCRIPTIVE STATISTICS

FOR VARIABLE Y .......................................................................... I I 1 NUM 1 MEAN 1 STD 1STDERR 1 VAR I CV 1 MIN 1 MAX 1 ' - - - - - - - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

1A 1B 1C 1 I I I I I 1 I I I I I I I I I I

I - - + - - + - - - - ! I I I I I I I I I I I I I I I I

11 13 12 1 161 15.151 4.681 1.171 21.941 30.921 6.281 22.751 1 1 ; - - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ; I I I 1 19 1 161 24.661 4.721 1.181 22.27: 19.131 16.741 31.131 1 : - -+-- - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ;

1 14 12 1 161 16.281 4.711 1.181 22.171 28.92: 8.501 25.64: 1 1 ; - - - -+- - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - -+- - - - - - - ; I I I 19 1 161 25.551 5.091 1.271 25.911 19.921 17.791 33.181 I I I #- -+ - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

1 15 12 1 161 16.591 5.161 1.291 26.631 31.111 8.431 25.321 1 1 ; - - - -+-- - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - -+-- - - - - - ; I I

I 19 1 161 26.421 4.591 1.151 21.071 17.371 18.981 34.231 ' - -+ - -+ - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - ;

12 13 12 1 161 17.711 4.921 1.231 24.221 27.791 11.13; 25.78: 1 1 ; - - - - + - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - ; I I I , 19 1 161 29.551 4.601 1.151 21.141 15.56: 23.131 37.161 1 : - - + - - - - + - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - - ;

1 14 12 1 161 18.991 4.751 1.19: 22.571 25.021 11.581 27.511 1 1 ; - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - 1 I I I I 19 161 30.281 4.551 1.141 20.701 15.03: 21.721 37.791 1 ; - -+ - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -

1 15 12 1 161 19.711 4.901 1.221 23.971 24.831 13.051 27.941 1 ; - - - -+ - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - -+ - - - - - - - 1

I I a I 19 1 161 31.271 5.061 1.261 25.591 16.181 22.521 40.641 ..........................................................................

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC31 ---- EXAMPLE PLOTS

Plot of Y*Xl. Symbol is value of A.

NOTE: 32 obs hidden.

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC31 ---- EXAMPLE PLOTS

Plot of Y*X2. Symbol is value of A.

NOTE: 13 obs hidden.

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC31 ---- EXAMPLE PLOTS

Plot of Y*X3. Symbol is value of A .

NOTE: 7 obs hidden.

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC31 ---- NORMAL CUMULATIVE PROBABILITY FOR Y

Plot of Y*STRDNORM. Legend: A = 1 obs, B = 2 obs, etc.

AA A

AA AA

BBA ACB AB A

CCA AEA AC

DD AEA

I I

I I C

I I I CFB

25 + I BFC I I I AD I I I F I 0 AF I I AFF l I I B I

20 + CC I I I AFC I I C I

I I

t AEB I

I

I

I DD I

I

I

I CA I I

15 + AEA I

I I

I BCC I

I

I

t CA I

1

I

I AC I

I

I

I ABBA I

I

1

I AA I I

10 + A I

I I

I AA I

I

I

I AA I

I

I

I A I I

I A I

I

I

I I I

5 + I I

-+-----------+-----------+-----------+-----------+-----------+-----------+-

-3 -2 -1 0 1 2 3

RANK FOR VARIABLE Y

W

U

HI

El,

GG

*

mx

U

UU

0

CIt W

\m

a

w

U

;ss z

W

aw

3

aw

l4

01 W

2

P"r

WY

E

l4

1 W

l E

1 4 I

x

W

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC32 ---- EXAMPLE BAR CHARTS

FREQUENCY OF A GROUPED BY B

FREQUENCY

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC32 ---- EXAMPLE BAR CHARTS

MEAN OF Y BY A GROUPED BY B

Y MEAN

SYMBOL C

2 2

SYMBOL C

9 9

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- REGRESSION OF Y VERSUS X1

Model: MODEL1 Dependent Variable: Y

Analysis of Variance

Source

Model Error C Total

Root MSE Dep Mean C.V.

Variable DF

INTERCEP 1 X1 1

Sum of Mean DF Squares Square F Value Prob>F

5.79933 R-square 8.3833 22.67907 Adj R-sq 0-, 3800 25.57128

'.

Parameter Estimates

Parameter Standard T for HO: Estimate Error Parameter=O Prob > IT!

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- LISTING OF DATA WITH CASE STATISTICS

OBS Y X1 PRED RESID STUDENT PRESS COOKD

OBS

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- LISTING OF DATA WITH CASE STATISTICS

PRED RESID STUDENT PRESS H-LEV COOKD '

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- LISTING OF DATA WITH CASE STATISTICS

OBS Y PRED

15.2800 16.2665 17.2531 18.2396 19.2262 20.2127 21.1993 22.1858 23.1723 24.1589 25.1454 26.1320 27.1185 28.1051 29.0916 30.0782 15.2800 16.2665 17.2531 18.2396 19.2262 20.2127 21 .I993 22.1858 23.1723 24.1589 25.1454 26 .I320 27.1185 28.1051 29.0916 30.0782 15.2800 16.2665 17.2531 18.2396 19.2262 20.2127 21.1993 22.1858 23.1723 24.1589 25.1454 26.1320 27.1185 28 .lo51 29.0916 30.0782 15.2800 16.2665 17.2531 18.2396 19.2262 20.2127 21 .I993 22.1858

RESID

6.44323 8.34844 7.05931 9.26675 9.35681 7.61316 7.15448 7.48280 6.84355 7.91727 8.18276 8 .lo543 6.60734 6.59197 6.91668 7.71650

-6.19640 -7.83495 -6.04118 -5.76592 -6.05718 -7.26377 -6.28795 -6.04137 -6.56308 -5.42597 -6.14485 -4.93969 -6.23480 -6.81240 -5.13453 -4.75773 3.70014 3.41434 4.29324 3.52749 5.27021 3.01546 4.12036 5.41051 2.12321 4.91397 3.76369 2.81460 3.11210 4.28668 5.13457 0.96634

-2.22565 -1.71432 -3.32924 -3.23036 -4.58727 -3.80134 -3.71446 -3.19060

STUDENT

1.12173 1.45089 1.22502 1.60609 1.62009 1.31721 1.23724 1.29370 1 .I8318 1.36915 1.41576 1.40342 1.14517 1 .I4392 1.20206 1.34341

-1.07876 -1.36165 -1.04834 -0.99934 -1.04878 -1.25676 -1.08739 -1.04449 -1.13469 -0.93833 -1.06317 -0.85529 -1.08060 -1 .I8217 -0.89234 -0.82830 0.64418 0.59338 0.74502 0.61138 0.91252 0.52173 0.71254 0.93542 0.36708 0.84978 0.65118 0.48734 0.53938 0.74388 0.89234 0.16824

-0.38747 -0.29793 -0.57773 -0.55988 -0.79427 -0.65770 -0 -64235 -0.55162

PRESS

6.56798 8.48043 7.14955 9.36197 9.43427 7.66482 7.19593 7.52244 6.87981 7.96314 8.23829 8.17254 6.67523 6.67624 7.02603 7.86592

-6.31638 -7.95882 -6 .I1841 -5.82518 -6.10732 -7.31306 -6.32438 -6.07337 -6.59785 -5.45741 -6.18655 -4.98058 -6.29887 -6.89949 -5.21570 -4.84985 3.77178 3.46832 4.34812 3.56374 5.31384 3.03592 4.14423 5.43917 2.13445 4 . 94244 3.78923 2.83790 3 .I4408 4.34148 5.21575 0.98505

-2.26874 -1.74142 -3.37180 -3.26356 -4.62525 -3.82714 -3.73598 -3.20750

COOKD

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC52 ---- MULTIPLE LOGISTIC REGRESSION

EXPERIMENTAL UNITS ARE IDENTIFIED BY I

CATMOD PROCEDURE

Response: Y Weight Variable: COUNT Data Set: EXAMPLE2

Response Levels (R)= 2 Populations (S)= 36 Total Frequency (N)=* 464 Observations (Obs)= 72

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Cdnvergence Iteration Iteration Likelihood Criterion ................................................

0 0 643.24058 1.0000 1 0 637.15453 0.009462 2 0 637.15364 1.4032E-6 3 0 637.15364 3.256E-13

Parameter Estimates Iteration 1 2 3 4

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. INTERCEPT 1 0.28 0.5955 X1 1 1.68 0.1943 X2 1 0.64 0.4250 X3 1 2.72 0.0989

LIKELIHOOD RATIO 32 44.88 0.0650

ANALYSIS OF MAXIMUM LIKELIHOOD ESTIMATES

Standard Chi- Effect Parameter Estimate Error Square Prob ................................................................ INTERCEPT 1 -0.2546 0.4797 0.28 0.5955 X1 2 -0.1472 0.1134 1.68 0.1943 X2 3 -0.0379 0.0475 0.64 0.4250 X3 4 0.1882 0.1141 2.72 0.0989

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC53 ---- ONE-WAY ANOVA-TYPE LOGISTIC REGRESSION EXPERIMENTAL UNITS ARE IDENTIFIED BY I

CATMOD PROCEDURE

Response: Y Weight Variable: COUNT Data Set: EXAMPLE2

Response Levels (R)= 2 Populations (S)= 36 Total Frequency (N)= 464 Observations (Obs)= 72

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 ........................................................................

0 0 643.24058 1 .OOOO 0 0 1 0 639.99084 0.005052 0.1560 -0.0624 2 0 639.9908 6.7897E-8 0.1564 -0.0628 3 0 639.9908 8.882E-16 0.1564 -0.0628

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. INTERCEPT 1 2.82 0.0932 A 1 0.45 0.5006

LIKELIHOOD RATIO 34 47.71 0.0595

ANALYSIS OF MAXIMUM LIKELIHOOD ESTIMATES

Standard Chi- Effect Parameter Estimate Error Square Prob ................................................................ INTERCEPT 1 0.1564 0.0932 2.82 0.0932 A 2 -0.0628 0.0932 0.45 0.5006

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC54 ---- ONE-WAY ANCOVA-TYPE LOGISTIC REGRESSION EXPERIMENTAL UNITS ARE IDENTIFIED BY I

CATMOD PROCEDURE

Response: Y Weight Variable: COUNT Data Set: EXAMPLE2

Response Levels (R)= 2 Populations (S)= 36 Total Frequency (N)= 464 Observations (Obis)= 72

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 3 ..............................................................................

0 0 643.24058 1.0000 0 0 0 1 0 639.94474 0.005124 0.0698 -0.0619 0.0116 2 0 639.9447 7.5066E-8 0.0696 -0.0623 0.0116 3 0 639.9447 7.106E-16 0.0696 -0.0623 0.0116

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. INTERCEPT 1 0.03 0.8667 A 1 0.45 0.5037 X1 1 0.05 0.8300

LIKELIHOOD RATIO 3 3 47.67 0.0474

ANALYSIS OF MAXIMUM LIKELIHOOD ESTIMATES

Standard Chi- Effect Parameter Estimate Error Square Prob ................................................................ INTERCEPT 1 0.0696 0.4149 0.03 0.8667 A 2 -0.0623 0.0932 0.45 0.5037 X1 3 0.0116 0.0542 0.05 0.8300

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC55 ---- ONE-WAY ANCOVA-TYPE LOGISTIC REGRESSION EXPERIMENTAL UNITS ARE IDENTIFIED BY I

CATMOD PROCEDURE

Response: Y Weight Variable: COUNT Data Set: EXAMPLE2

Response Levels (R)= 2 Populations (S)= 36 Total Frequency (N)= 464 Observations (Obs)= 72

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Convergence Iteration Iteration Likelihood Criterion ...............................................

0 0 643.24058 1.0000 1 0 614.72474 0.0443 2 0 614.61042 0.000186 3 0 614.61037 6.8222E-8 4 0 614.61037 1.147E-14

Parameter Estimates Iteration 1 2 3 4 5 6 ...........................................................................

0 0 0 0 0 0 0 1 0.1613 -0.0606 0.5725 -0.3370 0.2878 -0.0637 2 0.1764 -0.0496 0.6054 -0.3532 0.3134 -0.0759 3 0.1767 -0.0493 0.6059 -0.3535 0.3140 -0.0762 4 0.1767 -0.0493 0.6059 -0.3535 0.3140 -0.0762

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. INTERCEPT 1 3.37 0.0663 A 1 0.26 0.6083 B 2 18.94 0.0001 A*B 2 5.49 0.0642

LIKELIHOOD RATIO

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC55 ---- ONE-WAY ANCOVA-TYPE LOGISTIC REGRESSION EXPERIMENTAL UNITS ARE IDENTIFIED BY I

ANALYSIS OF MAXIMUM LIKELIHOOD ESTIMATES

Standard Effect Parameter Estimate Error ................................................. INTERCEPT 1 0.1767 0.0962 A 2 -0.0493 0.0962 B 3 0.6059 0.1401

4 -0.3535 0.1334 A*B 5 0.3140 0.1401

6 -0.0762 0.1334

Chi- Square Prob

, - - - - - - - - - - - - - - -

3.37 0.0663 0.26 0.6083

18.70 0.0000 7.02 0.0081 5.02 0.0250 0.33 0.5679

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- TWO-WAY TABLE OF SPECIES BY TRAP

(TABLE COMBINED OVER SEX)

TABLE OF SPECIES BY TRAP

SPECIES TRAP

Frequency I I

Cell Chi-square: 1 1 2 1 3 1 4 1 Total - - - - - - - - - - - - - - -+-- - - - - - -+-- - - - - - -+-- - - - - - -+-- - - - - - -+

SPP 1 I I 62 1 93 1 77 1 51 1 283 : 0.6153 : 0.0916 1 0.1423 1 0.863 1

---------------+--------+--------+--------+--------+

SPP 2 I I 49 : 53 1 40 1 30 1 172 1 1.3057 1 0.4861 1 0.5203 ! 0.2843 1

---------------+--------+--------+--------+-&------+

SPP 3 I I 71 1 109 1 79 1 38 1 297 : 0.0108 1 0.6821 1 0.0327 1 1.7229 1

- - - - - - - - - - - - - - -+ - - - - - - - -+ - - - - - - - -+ - - - - - - - -+ - - - - - - - -+

Total 182 255 196 119 752

STATISTICS FOR TABLE OF SPECIES BY TRAP

Statistic DF Value Prob ...................................................... Chi-square 6 6.757 0.344 Likelihood Ratio Chi-square 6 6.798 0.340 Mantel-Haenszel Chi-square 1 2.391 0.122 Phi Coefficient 0.095 Contingency Coefficient 0.094 Cramer's V 0.067

Sample Size = 752

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- TWO-WAY TABLES OF SPECIES BY TRAP

(SEPARATE TABLES FOR EACH SEX)

TABLE OF SPECIES BY TRAP

SPECIES TRAP

Frequency I I

Cell Chi-square: 1 1 2 1 3 1 41 Total - - - - - - - - - - - - - - -+-- - - - - - -+-- - - - - - -+-- - - - - - -+-- - - - - - -+

SPP 1 I I 32 1 45 1 34 1 20 1 131 : 0.0012 1 0.08 1 0.0705 1 0.0107 1

- - - - - - - - - - - - - - -+- - - - - - - -+- - - - - - - -+- - - - - - - -+- - - - - - - -+

SPP 2 I I 23 1 24 1 17 : 17 1 81 1 0.5653 1 0.2683 1 1.1373 1 1.4908 1

- - - - - - - - - - - - - - -+ - - - - - - - -+ - - - - - - - -+ - - - - - - - -+ - - - - - - - -+

SPP 3 I I 46 1 68 1 62 1 28 1 204 1 0.2514 1 0.0099 ) 0.7829 1 0.4711 :

- - - - - - - - - - - - - - - + - - - - - - - - + - - - - - - - - + - - - - - - - - + - - - - - - - - +

Total 101 137 113 65 416

STATISTICS FOR TABLE OF SPECIES BY TRAP

Statistic DF Value Prob ...................................................... Chi-square 6 5.140 0.526 Likelihood Ratio Chi-square 6 5.068 0.535 Mantel-Haenszel Chi-square 1 0.078 0.780 Phi Coefficient 0.111 Contingency Coefficient 0.110 Cramer's V 0.079

Sample Size = 416

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- TWO-WAY TABLES OF SPECIES BY TRAP

(SEPARATE TABLES FOR EACH SEX)

TABLE OF SPECIES BY TRAP

SPECIES TRAP

Frequency I I

Cell Chi-square; 1 1 2 1 3 1 41 Total ---------------+--------+--------+--------+--------+

SPP 1 I I 30 1 48 1 43 1 31 1 152 1 1.2043 : 0.5424 1 0.7918 1 1.7678 1

- - - - - - - - - - - - - - -+- - - - - - - -+- - - - - - - -+- - - - - - - -+- - - - - - - -+

SPP 2 I I 26 1 29 1 23 1 13 1 91 1 0.7523 1 0.2738 : 0.0121 1 0.1806 1

- - - - - - - - - - - - - - -+- - - - - - - -+- - - - - - - -+- - - - - - - -+- - - - - - - -+

SPP 3 I I 25 41 1 17 1 10 1 93 I 0.297 1 2.1293 : 1.5531 1 1.637 1

- - - - - - - - - - - - - - -+ - - - - - - - -+ - - - - - - - -+ - - - - - - - -+ - - - - - - - -+

Total 81 118 83 54 336

STATISTICS FOR TABLE OF SPECIES BY TRAP

Statistic DF Value Prob ...................................................... Chi-square 6 11.141 0.084 Likelihood Ratio Chi-square 6 11.240 0.081 Mantel-Haenszel Chi-square 1 7.921 0.005 Phi Coefficient 0.182 Contingency Coefficient 0.179 Cramer's V 0.129

Sample Size = 336

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- THREE-WAY TABLE OF SEX*SPECIES*TRAP

USING PROC CATMOD WITHOUT THREE-WAY INTERACTION SPECIFIED

CATMOD PROCEDURE

Response: SEX*SPECIES*TRAP Weight Variable: COUNT Data Set: EXAMPLE3

Response Levels (R)= 24 Populations (S)= 1 Total Frequency (N)= 752 Observations (Obs)= 2 4

- RESPONSE- MATRIX

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- THREE-WAY TABLE OF SEX*SPECIES*TRAP

USING PROC CATMOD WITHOUT THREE-WAY INTERACTION SPECIFIED

- RESPONSE- MATRIX

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 ........................................................................

0 0 4779.793 1.0000 0 0 1 0 4644.5457 0.0283 -0.0319 0.3564 2 0 4636.345 0.001766 0.0226 0.3344 3 0 4636.3173 5 9626E-6 0.0238 0.3312 4 0 4636.3173 1.201E-10 0.0238 0.3312

Parameter Estimates Iteration 3 4 5 6 7 .....................................................................

0 0 0 0 0 0 1 0.0426 0.1290 -0.3138 0.1064 -0.1902 2 0.0571 0.1883 -0.3066 0.0932 -0.1619 3 0.0596 0.1880 -0.3067 0.0926 -0.1626 4 0.0596 0.1880 -0.3067 0.0926 -0.1626

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- THREE-WAY TABLE OF SEX*SPECIES*TRAP

USING PROC CATMOD WITHOUT THREE-WAY INTERACTION SPECIFIED

Parameter Estimates Iteration 8 9 10 11 12 .....................................................................

0 0 0 0 0 0 1 -0.1463 -0.1077 -0.001330 0.0572 0.1277 2 -0.1497 -0 .I271 -0.0437 0.0550 0.1308 3 -0.1458 -0.1299 -0.0372 0.0529 0.1306 4 -0.1458 -0.1299 -0.0372 0.0529 0.1306

Parameter Estimates Iteration 13 14 15 16 17

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. TRAP 3 42.59 0.0000 SPECIES 2 26.90 0.0000 SEX 1 5.41 0.0200 SEX*SPECIES 2 35.01 0.0000 SPECIES*TRAP 6 7.03 0.3179 SEX*TRAP 3 1.02 0.7954

LIKELIHOOD RATIO 6 9.21 0.1624

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- TWO-WAY TABLE OF SPECIES BY TRAP

USING PROC CATMOD

CATMOD PROCEDURE

Response: SEX*SPECIES*TRAP Weight Variable: COUNT Data Set: EXAMPLE3

Response Levels (R)= 24 Populations (S)= 1 Total Frequency (N)= 752 Observations (Obs)= 24

RESPONSE- MATRIX -

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 3 .............................................................................

0 0 4779.793 1.0000 0 0 1 0 4647.1523 0.0278 -0.0319 0.3564

d 0.0426

2 0 4644.1417 0.000648 0.003194 0.3401 3 0 4644.1406 2.35813-7 0.003379 0.3406 0.077 4 0 4644.1406 3.329E-14 0.003380 0.3406

0*077d 0.0775

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC6 ---- TWO-WAY TABLE OF SPECIES BY TRAP

USING PROC CATMOD

Iteration 4 Parameter Estimates

5 6 7

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. TRAP 3 48.24 0.0000 SPECIES 2 30.69 0.0000 SEX 1 5.09 0.0241 SEX*SPECIES 2 34.74 0.0000

LIKELIHOOD RATIO 15 17.03 0.3172

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC71 ---- ONE-WAY ANOVA -- WITH OR WITHOUT BALANCED DATA

Analysis of Variance Procedure Class Level Information

Class Levels Values

B 3 3 4 5

Number of observations in data set = 192

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC71 ---- ONE-WAY ANOVA -- WITH OR WITHOUT BALANCED DATA

Analysis of Variance Procedure

Dependent Variable: Y Sum of Mean

Source DF Squares Square F Value

Model 2 96.68986146 48.34493073 0.89

Error 189 10264.4010846 54.30900045

Corrected Total 191 10361.0909460

R-Square C .V. Root MSE Y Mean

Source

B

DF Anova SS Mean Square F Value Pr > F

2 96.68986146 48.34493073 0.89 0.4123

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC71 ---- ONE-WAY ANOVA -- WITH OR WITHOUT BALANCED DATA

Analysis of Variance Procedure

Dependent Variable: X2 Sum of Mean

Source DF Squares Square F Value

Model 2 0.19223239 0.09611619 0.00 0.999

Error 189 24716.7772231 130.77659906

Corrected Total 191 24716.9694555

R-Square C.V. Root MSE

0.000008 16.15132 11.43576

X2 Mea 1

Source

B

DF Anova SS Mean Square F Value Pr > F

2 0.19223239 0.09611619 0.00 0.999

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC71 ---- ONE-WAY ANOVA -- WITH OR WITHOUT BALANCED DATA

Analysis of Variance Procedure

Duncan's Multiple Range Test for variable: Y

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 3 Critical Range 2.588 2.721

Means with the same letter are not significantly different.

Duncan Grouping Mean N B

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC71 ---- ONE-WAY ANOVA -- WITH OR WITHOUT BALANCED DATA

Analysis of Variance Procedure

Duncan's Multiple Range Test for variable: X2

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 3 Critical Range 4.016 4.223

Means with the same letter are not significantly different.

Duncan Grouping Mean N B

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- ONE-WAY ANCOVA

General Linear Models Procedure Class Level Information

Class Leve 1 s Values

Number of observations in data set = 192

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- ONE-WAY ANCOVA

General Linear Models Procedure

Dependent Variable: Y Sum of Mean

Source DF Squares Square F Value I

Model 3 4188.354445 1396.118148 42.52 0.000

Error 188 6172.736502 32.833705 1 - Corrected Total 191 10361.090946

R-Square C.V. Root MSE Y Meai

Source DF Type I SS Mean Square F Value Pr > F

Source DF Type I11 SS Mean Square F Value Pr >

Parameter T for HO: Pr > iTI Std Error of

Estimate Parameter=O Estimate

INTERCEPT -?+- ' -5.322048504 B -1.99 0.0484 2.67912711 B -1.701273060 B -1.68 0.0947 1.01294627

4 -0.718951451B -0.71 0.4787 1.01294296 5 0.000000000 B

X2 0.406868522 11.16 0.0001 0.03644719

NOTE: The X'X matrix has been found to be singular and a generalized inverse was used to solve the normal equations. Estimates followed by the letter 'B' are biased, and are not unique estimators of the parameters.

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- ONE-WAY ANCOVA

General Linear Models Procedure

Duncan's Multiple Range Test for variable: Y

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 3 Critical Range 2.012 2.116

Means with the same letter are not significantly different.

Duncan Grouping Mean N B

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- ONE-WAY ANCOVA

General Linear Models Procedure Least Squares Means

B Y Std Err Pr > IT I LSMEAN LSMEAN LSMEAN HO:LSMEAN=O Number

Pr > IT: HO: LSMEAN(i)=LSMEAN(j)

NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- PLOT OF PREDICTED AND ACTUAL VALUES

Plot of YfX2. Symbol is value of B . Plot of PY*X2. Symbol used is ' + ' .

NOTE: 96 obs hidden.

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- PLOT OF PREDICTED AND ACTUAL VALUES

Plot of PY*X2. Symbol is value of B.

NOTE: 63 obs hidden.

OBS Y

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- LISTING OF DATA WITH CASE STATISTICS

PRED RESID STUDENT PRESS COOKD

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- PRESS SUM OF SQUARES -- REF: COOK AND WEISBERG

N Obs Variable Label N Sum

192 PRESS Residual without Current Observation 192 0.0263800 STUDENT Studentized Residual 192 0.0022580 PRED Predicted Value of Y 192 4354.38

N Obs Variable Label

192 PRESS Residual without Current Observation STUDENT Studentized Residual PRED Predicted Value of Y 102724.31

N Obs Variable Label

192 PRESS STUDENT Studentized Residual PRED Predicted Value of Y 3970.97

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- PLOTS FOR THE REGRESSION OF Y VERSUS X1

Plot of Y*Xl. Symbol u s e d i s ' * ' . Plot of PRED'X1. Symbol used i s ' + ' .

w

am

aa

n

aa

. .

I

W 4

I

1 I

I u

C)

I I

t I

w m

I

I I

I w

m

I I

I I

mw

I

I I

I u

ua

I I

I -- +

-------------------------------------------- m a -

-a

m ---------------------------------------- +

+O

I

I m

na

I

I I

I a k

l I

I I

I u

n

I I

I I

w m

I

I I

I U

U

I I

1 I

lu

I I

I I

U U

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I I

I a

n

I I

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC4 ---- PLOTS FOR THE REGRESSION OF Y VERSUS X I

P l o t of STUDENT'PRED. Legend: A = 1 obs, B = 2 obs, e t c .

I I

2.0 + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I

I A I I A A I A A A I A A A

1.5 + A ! A B A A A A A I I A B A A A A I A A A A A A A I I A A B A A B A A A I A A

1 .0 + A I I A A A A A

3 I I A I

i I A A A B A 1 I A A A A i I A B A B A A P 0 . 5 + A A B A A A 1 I A A A A t I

I A B A A L I A A A L I

I A B 2 I

I A A

1 I A A B B A A A L I A A A B

I A C A A B A A A A I A A A A

-1.0 + A B A A B A A A I A A A A B A A A A I A B A B I A B A A A A A I A A A A A I A A

-1.5 + A A A I A A I I I

I I I I

-2.0 + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

P r e d i c t e d V a l u e o f Y

EXAMPLE FOR S A S / P C P R A C T I C E ---- PROGRAM SEC4 ---- P L O T S FOR THE REGRESSION OF Y VERSUS X 1

P l o t of STUDENT'X l . Legend: A = 1 o b s , B = 2 obs, e t c .

I I

+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I I 1 A I \$ A A I 1 A A A I A A A + A I A B A A A A A I I A B A A A A I A A A A A A A I I A A B A A B A A A I A A + A I A A A A A I 1 A I I A A A B A I A A A A I A B A B A A + A A B A A A I A A A A I I A B A A I A A A I A B I I A A A + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - A - - - - - - - - - - - - I I I A I I A A I I A A

A A A A + A A I A B A A A B A 1 A A B B A A A I A A A B 1 A C A A B A A A A I A A A A + A B A A B A A A I A A A A B A A A A I A B A B I A B A A A A A I A A A A A I A A + A A A I A A I I I

I I I I

+- - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - + - - - - - - - -

0 2 4 6 8 10 1 2 1 4 16 1 8 2 0 2 2 2 4 2 6 2 8 30

EXAMPLE FOR SAS/PC PRACTICE ---- PROGRAM SEC41 ---- REGRESSION OF Y VERSUS X1, X2, AND X3

N = 192 Regression Models for Dependent Variable: Y

C(p) R-square Adjusted MSE Variables in Model In R-square

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC51 ---- SIMPLE LOGISTIC REGRESSION

EXPERIMENTAL UNITS ARE IDENTIFIED BY I

CATMOD PROCEDURE

Response: Y Weight Variable: COUNT Data Set: EXAMPLE2

Response Levels ( R ) = 2 Populations (S)= 36 Total Frequency (N)= 464 Observations (Obs)= 72

POPULATION PROFILES Sample

Sample I Size .................... 1 1 13 2 2 15 3 3 15 4 4 10 5 5 11 6 6 13 7 7 15 8 8 11 9 9 15

10 10 13 11 11 15 12 12 11 13 13 15 14 14 13 15 15 10 16 16 15 17 17 13 18 18 12 19 19 10 20 20 14 21 21 15 22 22 13 23 23 13 24 24 10 25 25 14 26 26 13 27 27 12 28 28 10 29 29 14 30 30 15 31 31 15 32 32 12 33 33 10 34 34 14 35 35 10 36 36 15

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC51 ---- SIMPLE LOGISTIC REGRESSION

EXPERIMENTAL UNITS ARE IDENTIFIED BY I

RESPONSE PROFILES

Response Y ----------- 1 0 2 1

MAXIMUM LIKELIHOOD ANALYSIS

Sub -2 Log Convergence Parameter Estimates Iteration Iteration Likelihood Criterion 1 2 ........................................................................

0 0 643.24058 1.0000 0 0 1 0 640.392 0.004428 0.0630 0.0124 2 0 640.39198 2.2678E-8 0.0627 0.0124 3 1 640.39198 1.775E-16 0.0627 0.0124

MAXIMUM LIKELIHOOD ANALYSIS OF VARIANCE TABLE

Source DF Chi-square Prob .................................................. INTERCEPT 1 0.02 0.8797 X1 1 0.05 0.8185

LIKELIHOOD RATIO 34 48.11 0.0550

ANALYSIS OF MAXIMUM LIKELIHOOD ESTIMATES

Standard Chi- Effect Parameter Estimate Error Square Prob ................................................................ INTERCEPT 1 0.0627 0.4146 0.02 0.8797 X1 2 0.0124 0.0542 0.05 0.8185

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC51 ---- SIMPLE LOGISTIC REGRESSION

EXPERIMENTAL UNITS ARE IDENTIFIED BY I

MAXIMUM LIKELIHOOD PREDICTED VALUES FOR RESPONSE FUNCTIONS AND FREQUENCIES

------- Observed------- ------- Predicted------ Function Standard Standard

Sample Number Function Error Function Error Residual .......................................................................... 1 1 1.70474809 0.76870611 0.12492202 0.16242961 1.57982607

F1 11 1.30088727 6.90546942 0.52584206 4.09453058 F2 2 1.30088727 6.09453058 0.52584206 -4.0945306

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC51 ---- SIMPLE LOGISTIC REGRESSION

EXPERIMENTAL UNITS ARE IDENTIFIED BY I

MAXIMUM LIKELIHOOD PREDICTED VALUES FOR RESPONSE FUNCTIONS AND FREQUENCIES

------- Observed------- ------- Predicted------ Function Standard Standard

Sample Number Function Error Function Error Residual .......................................................................... 13 1 -0.1335314 0.51754917 0.12492202 0.16242961 -0.2584534

F1 7 1.93218357 7.96784933 0.60674084 -0.9678493 F2 8 1.93218357 7.03215067 0.60674084 0.96784933

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC51 ---- SIMPLE LOGISTIC REGRESSION

EXPERIMENTAL UNITS ARE IDENTIFIED BY I

MAXIMUM LIKELIHOOD PREDICTED VALUES FOR RESPONSE FUNCTIONS AND FREQUENCIES

------- Observed------- - - - - - -A Predicted------ Function Standard Standard

Sample Number Function Error Function Error Residual .......................................................................... 25 1 0.28768207 0.54006172 0.12492202 0.16242961 0.16276005

€1 8 1.8516402 7.43665938 0.56629145 0.56334062 F2 6 1.8516402 6.56334062 0.56629145 -0.5633406

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- PLOT OF PREDICTED AND ACTUAL VALUES

Plot of Y*X2. Symbol is value of B. Plot of PY*X2. Symbol used is I + ' .

NOTE: 2 5 obs hidden.

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- PLOT OF PREDICTED AND ACTUAL VALUES

Plot of Y*X2. Symbol is value of B. Plot of PY*X2. Symbol used is ' + ' .

NOTE: 50 obs hidden.

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC72 ---- PLOT OF PREDICTED AND ACTUAL VALUES

Plot of Y*X2. Symbol is value of B. Plot of PY*X2. Symbol used is ' + I .

NOTE: 71 obs hidden.

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC72 ---- ONE-WAY ANCOVA

TESTING FOR HETEROGENEITY OF REGRESSION

General Linear Models Procedure Class Level Information

Class Level s Values

Number of observations in data set = 192

EXAMPLE CONTINGENCY TABLES ANALYSIS ---- PROGRAM SEC72 ---- ONE-WAY ANCOVA

TESTING FOR HETEROGENEITY OF REGRESSION

General Linear Models Procedure

Dependent Variable: Y Sum of Mean

Source DF Squares Square F Value Pr > F

Mode 1 5 4191.435911 838.287182 25.27 0.0001

Error 186 6169.655035 33.170188

Corrected Total 191 10361.090946

R-Square C.V. Root MSE Y Mean

Source DF Type I SS Mean Square F Value Pr > F

Source DF Type I11 SS Mean Square F Value Pr > F

Parameter

INTERCEPT B 3

4 5

X2 X2*B 3

4 5

T for HO: Pr > IT: Std Error of Estimate Parameter=O Estimate

NOTE: The X'X matrix has been found to be singular and a generalized inverse was used to solve the normal equations. Estimates followed by the letter 'B' are biased, and are not unique estimators of the parameters.

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC73 ---- TWO-WAY ANOVA

General Linear Models Procedure Class Level Information

Class Levels Values

A 2 1 2

B 3 3 4 5

Number of observations in data set = 192

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC73 ---- TWO-WAY ANOVA

General Linear Models Procedure

Dependent Variable: Y Sum of Mean

Source DF Squares Square F Value Pr > F

Model 5 793.7273915 158.7454783 3.09 0.0106

Error 186 9567.3635545 51.4374385

Corrected Total 191 10361.0909460

R-Square C.V. Root MSE Y Mean

Source

Source

Dl? Type I SS Mean Square F Value Pr > F

DF Type I11 SS Mean Square F Value Pr > F

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC73 ---- TWO-WAY ANOVA

General Linear Models Procedure

Duncan's Multiple Range Test for variable: Y

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 Critical Range 2.056

Means with the same letter are not significantly different.

Duncan Grouping

A

Mean N A

2 4 . 5 8 3 96 2

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC73 ---- TWO-WAY ANOVA

General Linear Models Procedure

Duncan's Multiple Range Test for variable: Y

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 3 Critical Range 2.519 2.648

Means with the same letter are not significantly different.

Duncan Grouping Mean N B

Level of Level of --------------y-------------- A B N Mean SD

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC73 ---- TWO-WAY ANOVA

CUMULATIVE PROBABILITY PLOT OF RESIDUALS FROM ANOVA

Plot of RY*STDNRMY. Legend: A = 1 obs, B = 2 obs, etc.

RY I I

, I

I I I

15 + I I A

I I

I

I

I

I I 4 A A

I I

I 4 AAA

I I

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-3 -2 -1 0 1 2 3 RANK FOR VARIABLE RY

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC74 ---- TYPICAL SPLIT-PLOT DESIGN

WITH SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure Class Level Information

Class Level s Values

Number of observations in data set = 192

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC74 ---- TYPICAL SPLIT-PLOT DESIGN

WITH SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure

Dependent Variable: Y

Source DF Sum of

Squares Mean

Square F Value

Model 11 6188.481972 562.589270 24.27 0.0001

Error 180 4172.608974 23 .I81161 I Corrected Total 191 10361.090946 -

R-Square C.V. Root MSE I Y Mean

Source DF Type I SS Mean Square F Value

Source DF Type I11 SS Mean Square F Value

Tests of Hypotheses using the Type I11 MS for B*A as an error term

Source DF Type I11 SS Mean Square F Value

Tests of Hypotheses using the Type I11 MS for B*A*C as an error term

Source DF Type I11 SS Mean Square F Value

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC74 ---- TYPICAL SPLIT-PLOT DESIGN

WITH SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure

Duncan's Multiple Range Test for variable: Y

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 Critical Range 0.386

Means with the same letter are not significantly different.

Duncan Grouping Mean N A

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC74 ---- TYPICAL SPLIT-PLOT DESIGN

WITH SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure

Duncan's Multiple Range Test for variable: Y

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 Critical Range 0.316

Means with the same letter are not significantly different.

Duncan Grouping Mean N C

Level of Level of --------------y-------------- A C N Mean SD

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC741 ---- TYPICAL SPLIT-PLOT DESIGN

WITHOUT SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure Class Level Information

Class Level s Values

Number of observations in data set = 12

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC741 ---- TYPICAL SPLIT-PLOT DESIGN

WITHOUT SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure

Dependent Variable: MEANY Sum of Mean

Source DF Squares Square F Value ~r > I Model 7 386.6250332 55.2321476 1424.52 0.0001

Error 4 0.1550900 0.0387725 I Corrected Total 11 386.7801233

R-Square C.V. Root MSE MEANY Mea d

Source DF Type I SS Mean Square F Value

2 6.0431163 3.0215582 77.93 Pr > Fl 0.0006 1 43.5165127 43.5165127 1122.35 2 0.0483329 0.0241665 0.62 1 333.9431464 333.9431464 8612.89

::::q 0.0001

1 3.0739249 3.0739249 79.28 0.0009

Source DF Type I11 SS Mean Square F Value Pr >

Tests of Hypotheses using the Type I11 MS for B*A as an error term

Source DF Type I11 SS Mean Square F Value Pr > 4 A 1 43.51651271 43.51651271 1800.70 0. o o o q

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC741 ---- TYPICAL SPLIT-PLOT DESIGN

WITHOUT SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure

Duncan's Multiple Range Test for variable: MEANY

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 Critical Range 0.386

Means with the same letter are not significantly different.

Duncan Grouping Mean N A

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC741 ---- TYPICAL SPLIT-PLOT DESIGN

WITHOUT SUBSAMPLING WITHIN SPLIT-PLOT

General Linear Models Procedure

Duncan's Multiple Range Test for variable: MEANY

NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate

Number of Means 2 Critical Range 0.316

Means with the same letter are not significantly different.

Duncan Grouping Mean N C

Level of Level of ------------ MEANY------------ A C N Mean SD

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC751 ---- TWO-WAY ANOVA

WITH ORTHOGONAL POLYNOMIAL CONTRASTS

General Linear Models Procedure Class Level Information

Class Leve 1 s Values

Number of observations in data set = 60

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC751 ---- TWO-WAY ANOVA

WITH ORTHOGONAL POLYNOMIAL CONTRASTS

General Linear Models Procedure

Dependent Variable: Y Sum of Mean

Source DF Squares Square F Value Pr >

Model 19 3740.670683 196.877404 147.84 0.0001 1 Error 40 53.267614 1.331690

Corrected Total 59 3793.938297

R-Square C.V. Root MSE Y Meam I

Source

Source

Type I SS

Type I11 SS

Mean Square

Mean Square

F Value

F Value

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC751 ---- TWO-WAY ANOVA

WITH ORTHOGONAL POLYNOMIAL CONTRASTS

General Linear Models Procedure

T tests (LSD) for variable: Y

NOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate.

Alpha= 0.05 df= 40 MSE= 1.33169 Critical Value of T= 2.02

Least Significant Difference= 0.9522

Means with the same letter are not significantly different.

T Grouping Mean N A

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC751 ---- TWO-WAY ANOVA

WITH ORTHOGONAL POLYNOMIAL CONTRASTS

General Linear Models Procedure

T tests (LSD) for variable: Y

NOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate.

Alpha= 0.05 df= 40 MSE= 1.33169 Critical Value of T= 2.02

Least Significant Difference= 0.8516

Means with the same letter are not significantly different.

T Grouping Mean N B

Level of Level of --------------y-------------- A B N Mean SD

ANALYSIS OF EXAMPLE DATASET ---- PROGRAM SEC751 ---- TWO-WAY ANOVA

WITH ORTHOGONAL POLYNOMIAL CONTRASTS

General Linear Models Procedure

Dependent Variable: Y

Contrast DF Contrast SS Mean Square F Value Pr > F