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

426 CHAPTER 13 | Repeated-Measures Analysis of Variance
For the example we are considering, the F-ratio has df = 2, 10 (“degrees of freedom equal
two and ten”). Using the F distribution table (p. 653) with α = .05, the critical value is
F = 4.10, and with α = .01 the critical value is F = 7.56. Our obtained F-ratio, F = 19.09,
is well beyond either of the critical values, so we can conclude that the differences between
treatments are significantly greater than expected by chance using either α = .05 or
α = .01.
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The summary table for the repeated-measures ANOVA from Example 13.1 is presented
in Table 13.3. Although these tables are no longer commonly used in research reports, they
provide a concise format for displaying all of the elements of the analysis.
TABLE 13.3
A summary table for
the repeated-measures
ANOVA for the data from
Example 13.1.
Source SS df MS F
Between treatments 84 2 42.00 F(2, 10) = 19.09
Within treatments 88 15
Between subjects 66 5
Error 22 10 2.20
Total 172 17
The following example is an opportunity to test your understanding of the calculation of SS
values for the repeated-measures ANOVA.
EXAMPLE 13.2
For the following data, compute SS between treatments
and SS between subjects
.
Treatment
Subject 1 2 3 4
A 2 2 2 2 G = 32
B 4 0 0 4 ΣX 2 = 96
C 2 0 2 0
D 4 2 2 4
T = 12 T = 4 T = 6 T = 10
You should find that SS between treatments
= 10 and SS between subjects
= 8.
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■ Measuring Effect Size for the Repeated-Measures ANOVA
The most common method for measuring effect size with ANOVA is to compute the
percentage of variance that is explained by the treatment differences. In the context of
ANOVA, the percentage of variance is commonly identified as η 2 (eta squared). In
Chapter 12, for the independent-measures analysis, we computed η 2 as
2 5
SS between treatments
SS between treatments
1 SS within treatments
5 SS between treatments
SS total
The intent is to measure how much of the total variability is explained by the differences
between treatments. With a repeated-measures design, however, there is another component
that can explain some of the variability in the data. Specifically, part of the variability
is caused by differences between individuals. In Table 13.2, for example, person C consistently
scored higher than person A or B. This consistent difference explains some of the
variability in the data. When computing the size of the treatment effect, it is customary to