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The Completely Randomized Design (CRD). Lab # 1. Definition. Achieved when the samples of experimental units for each treatment are random and independent of each other Design is used to compare the treatment means:. The hypotheses are tested by comparing the differences - PowerPoint PPT Presentation
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THE COMPLETELY RANDOMIZED DESIGN (CRD)
LAB # 1
DEFINITIONAchieved when the samples of
experimental units for each treatment are random and independent of each other
Design is used to compare the treatment means:
0 1 2: ... kH :aH At least two of the treatment means differ
•The hypotheses are tested by comparing the differences between the treatment means.
•Test statistic is calculated using measures of variability within treatment groups and measures of variability between treatment groups
STEPS FOR CONDUCTING AN ANALYSIS OF VARIANCE (ANOVA) FOR A COMPLETELY RANDOMIZED DESIGN:
•1 -Assure randomness of design, and independence, randomness of samples
•2 -Check normality, equal variance assumptions
•3 -Create ANOVA summary table
•4 -Conduct multiple comparisons for pairs of means as necessary/desired
ASSUMPTIONS
1 -Normality :
You can check on normality using
1 -plot
2 -Kolmogorve test
2 -Constant variance:
You can check on homogeneity of variances using
1 -Plot2 -leven’s test.
ONE WAY ANOVA
ANOVA Summary Table for a Completely Randomized Design
Source df SS MS F
Treatments 1k SST 1
SSTMST
k
MST
MSE
Error n k SSE SSE
MSEn k
Total 1n SS Total
MULTIPLE COMPARISONS OF MEANS
•A significant F-test in an ANOVA tells you that the treatment means as a group are statistically different.
•Does not tell you which pairs of means differ statistically from each other
•With k treatment means, there are c different pairs of means that can be compared, with c calculated as
1
2
k kc
MULTIPLE COMPARISONS OF MEANS
Guidelines for Selecting a Multiple Comparisons Method in ANOVA
Method Treatment Sample Sizes Types of Comparisons Tukey Equal Pairwise Bonferroni Equal or Unequal Pairwise Scheffe Equal or Unequal General Contrasts
EXAMPLE 1
A manufacturer of television sets is interested in the effect on tube conductivity of four different types of coating for color picture tubes. The
following conductivity data are obtained.
CoatingConductivity
1146150141143
2143137149152
3127132136134
4129132127129
SOLUTION
Enter data in spss as follows:
ANALYSIS
Test of Homogeneity of Variances
conductiivity
Levene Statisticdf1df2Sig.
2.370312.122
Tests of Normality
Kolmogorov-SmirnovaShapiro-Wilk
StatisticdfSig.StatisticdfSig.
conductiivity.13316.200*.92816.230
a. Lilliefors Significance Correction
*. This is a lower bound of the true significance.
ONE WAY ANOVA
ANOVA
conductiivity
Sum of SquaresdfMean SquareFSig.
Between Groups844.6883281.56214.302.000
Within Groups236.2501219.688
Total1080.93815
Multiple Comparisons
Dependent Variable:conductiivity
(I) coating(J) coating
Mean Difference (I-
J)Std. ErrorSig.
95% Confidence Interval
Lower BoundUpper Bound
Tukey HSD12-.250-3.1371.000-9.56-9.06
312.750*3.137.0073.4422.06
415.750*3.137.0016.4425.06
21.2503.1371.000-9.06-9.56
313.000*3.137.0063.6922.31
416.000*3.137.0016.6925.31
31-12.750*3.137.007-22.06--3.44-
2-13.000*3.137.006-22.31--3.69-
43.0003.137.776-6.31-12.31
41-15.750*3.137.001-25.06--6.44-
2-16.000*3.137.001-25.31--6.69-
3-3.000-3.137.776-12.31-6.31
LSD12-.250-3.137.938-7.09-6.59
312.750*3.137.0025.9119.59
415.750*3.137.0008.9122.59
21.2503.137.938-6.59-7.09
313.000*3.137.0016.1619.84
416.000*3.137.0009.1622.84
31-12.750*3.137.002-19.59--5.91-
2-13.000*3.137.001-19.84--6.16-
43.0003.137.358-3.84-9.84
41-15.750*3.137.000-22.59--8.91-
2-16.000*3.137.000-22.84--9.16-
3-3.000-3.137.358-9.84-3.84
Thanks for all
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