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

420 CHAPTER 13 | Repeated-Measures Analysis of Variance
13.2 Hypothesis Testing and Effect Size
with the Repeated-Measures ANOVA
LEARNING OBJECTIVES
2. Describe the two-stage structure of the repeated-measures ANOVA and explain what
happens in each stage.
3. Calculate all of the SS, df, and MS values needed for a repeated-measures ANOVA
and explain the relationships among them.
4. Conduct a complete repeated-measures ANOVA and a measure of effect size.
5. Describe how the results of a repeated-measures ANOVA are reported in the
literature and explain how to determine the number of treatments and the number
of participants from the reported df values for the F-ratio.
The overall structure of the repeated-measures ANOVA is shown in Figure 13.2. Note
that the ANOVA can be viewed as a two-stage process. In the first stage, the total variance
is partitioned into two components: between-treatments variance and within-treatments
variance. This stage is identical to the analysis that we conducted for the independentmeasures
design in Chapter 12.
The second stage of the analysis is intended to remove the individual differences from
the denominator of the F-ratio. In the second stage, we begin with the variance within treatments
and then measure and subtract out the between-subject variance, which measures the
size of the individual differences. The remaining variance, often called the residual variance,
or error variance, provides a measure of how much variance is reasonable to expect
Total
variance
Stage 1
Between-treatments
variance
1. Treatment effect
2. Error or chance
(excluding individual
differences)
Within-treatments
variance
1. Individual
differences
2. Other error
Numerator of
F-ratio
Stage 2
FIGURE 13.2
The partitioning
of variance for a
repeated-measures
research study.
Between-subjects
variance
1. Individual
differences
Error
variance
1. Error (excluding
individual
differences)
Denominator of
F-ratio