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

436 CHAPTER 13 | Repeated-Measures Analysis of Variance
SUMMARY
1. The repeated-measures ANOVA is used to evaluate
the mean differences obtained in a research study
comparing two or more treatment conditions using the
same sample of individuals in each condition. The test
statistic is an F-ratio, where the numerator measures
the variance (differences) between treatments and the
denominator measures the variance (differences)
that are expected without any treatment effects or
individual differences.
F 5 MS between treatments
MS error
2. The first stage of the repeated-measures ANOVA is
identical to the independent-measures analysis and
separates the total variability into two components:
between-treatments and within-treatments. Because
a repeated-measures design uses the same subjects in
every treatment condition, the differences between
treatments cannot be caused by individual differences.
Thus, individual differences are automatically
eliminated from the between-treatments variance in
the numerator of the F-ratio.
3. In the second stage of the repeated-measures analysis,
individual differences are computed and removed
from the denominator of the F-ratio. To remove
the individual differences, you first compute the
variability between subjects (SS and df) and then
subtract these values from the corresponding withintreatments
values. The residual provides a measure of
error excluding individual differences, which is the
appropriate denominator for the repeated-measures
F-ratio. The equations for analyzing SS and df for the
repeated-measures ANOVA are presented in
Figure 13.3.
4. Effect size for the repeated-measures ANOVA is
measured by computing eta squared, the percentage of
variance accounted for by the treatment effect. For the
repeated-measures ANOVA
SS between treatments
2 5
SS total 2 SS between subjects
SS between treatments
5
SS between treatments
1 SS error
Because part of the variability (the SS due to individual
differences) is removed before computing η 2 , this measure
of effect size is often called a partial eta squared.
G 2
SS total = SX 2 – —
N
df total = N 2 1
SS between treatments = SS total 2 SS within treatments
= S T 2 G
— 2
or, SS between treatments 2 —
n N
SS within treatments = SSS inside each treatment
df within treatments = S(n 21)
df between treatments = k21
Numerator of F-ratio
SS between subjects = S
df between subjects = n 21
FIGURE 13.3
Formulas for the repeated-measures ANOVA.
P 2 G 2
k 2
N
SS error = SS within treatments 2 SS between subjects
df error = df within treatments 2 df between subjects
Denominator of F-ratio