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

SECTION 13.1 | Overview of the Repeated-Measures ANOVA 419
uses the same individuals in all treatments. In the denominator, the individual differences
are subtracted out during the analysis. As a result, the repeated-measures F-ratio has the
following structure:
between 2 treatments variance
F 5
error variance
treatment effects 1 random, unsystematic differences
5
random, unsystematic differences
(13.1)
Note that this F-ratio is structured so that there are no individual differences contributing
to either the numerator or the denominator. When there is no treatment effect, the F-ratio
is balanced because the numerator and denominator are both measuring exactly the same
variance. In this case, the F-ratio should have a value near 1.00. When research results produce
an F-ratio near 1.00, we conclude that there is no evidence of a treatment effect and
we fail to reject the null hypothesis. On the other hand, when a treatment effect does exist,
it contributes only to the numerator and should produce a large value for the F-ratio. Thus,
a large value for F indicates that there is a real treatment effect and therefore we should
reject the null hypothesis.
LEARNING CHECK
1. In an independent-measures ANOVA, individual differences contribute to the
variance in the numerator and in the denominator of the F-ratio. For a repeatedmeasures
ANOVA, what happens to the individual differences in the numerator of
the F-ratio?
a. They do not exist because the same individuals participate in all of the
treatments.
b. They are measured and subtracted out during the analysis.
c. Individual differences contribute to the variance in the numerator.
d. None of the other options accurately describes individual differences in the
numerator.
2. In an independent-measures ANOVA, individual differences contribute to the
variance in the numerator and in the denominator of the F-ratio. For a repeatedmeasures
ANOVA, what happens to the individual differences in the denominator
of the F-ratio?
a. They do not exist because the same individuals participate in all of the
treatments.
b. They are measured and subtracted out during the analysis.
c. Individual differences contribute to the variance in the numerator.
d. None of the other options accurately describes individual differences in the
numerator.
ANSWERS
1. A, 2. B