Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

440 CHAPTER 13 | Repeated-Measures Analysis of Variance
and the corresponding degrees of freedom are
df total
= N – 1 = 14
df within
= Σdf = 4 + 4 + 4 = 12
df between
= k – 1 = 2
STAGE 2
The second stage of the repeated-measures analysis measures and removes the individual
differences from the denominator of the F-ratio.
SS between subjects
5S P2
k 2 G2
N
5 62
3 1 92
3 1 62
3 1 182
3 1 62
3 2 452
15
5 36
SS error
= SS within
− SS between subjects
= 40 – 36
= 4
and the corresponding df values are
df between subjects
= n – 1 = 4
df error
= df within
− df between subjects
= 12 − 4
= 8
The mean square values that form the F-ratio are as follows:
Finally, the F-ratio is
MS between
5 SS between
df between
5 70 2 5 35
MS error
5 SS error
df error
5 4 8 5 0.50
F 5 MS between
MS error
5 35
0.50 5 70.00
STEP 3
Make a decision and state a conclusion With df = 2, 8 and α = .05, the critical value is
F = 4.46. Our obtained F-ratio (F = 70.00) is well into the critical region, so our decision
is to reject the null hypothesis and conclude that there are significant differences among the
three levels of sleep deprivation.
DEMONSTRATION 13.2
EFFECT SIZE FOR THE REPEATED-MEASURES ANOVA
We will compute η 2 , the percentage of variance explained by the treatment differences, for
the data in Demonstration 13.1. Using Equation 13.11 we obtain
h 2 5
SS between treatments
5 70
SS between treatments
1 SS error
70 1 4 5 70 5 0.95 sor 95%d
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