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

444 CHAPTER 13 | Repeated-Measures Analysis of Variance
Treatment
Subject I II III P
A 6 2 3 11 G = 48
B 5 1 5 11 ΣX 2 = 294
C 0 5 10 15
D 1 8 2 11
T = 12 T = 16 T = 20
SS = 26 SS = 30 SS = 38
a. Use a repeated-measures ANOVA with α = .05
to determine whether these data are sufficient to
demonstrate significant differences between the
treatments.
b. The data in problem 18 showed consistent differences
between subjects and produced significant
treatment effects. Explain how eliminating the consistent
individual differences affected the results
of this analysis compared with the results from
Problem 18.
20. A recent study indicates that simply giving college
students a pedometer can result in increased walking
(Jackson & Howton, 2008). Students were given
pedometers for a 12-week period, and asked to record
the average number of steps per day during weeks 1,
6, and 12. The following data are similar to the results
obtained in the study.
Number of steps (×1000)
Week
Participant 1 6 12 P
A 6 8 10 24
B 4 5 6 15
C 5 5 5 15 G = 72
D 1 2 3 6
E 0 1 2 3
ΣX 2 = 400
F 2 3 4 9
T = 18 T = 24 T = 30
SS = 28 SS = 32 SS = 40
a. Use a repeated-measures ANOVA with α = .05
to determine whether the mean number of steps
changes significantly from one week to another.
b. Compute η 2 to measure the size of the treatment
effect.
c. Write a sentence demonstrating how a research
report would present the results of the hypothesis
test and the measure of effect size.
21. One of the primary advantages of a repeated-measures
design, compared to independent-measures, is that
it reduces the overall variability by removing variance
caused by individual differences. In the previous
problem, the very large differences among the P totals
indicate very large individual differences. For the
repeated-measures ANOVA, removing these differences
greatly reduces the variance and results in a
significant F-ratio and a large value for η 2 . Assume
that the same data were obtained from an independentmeasures
study comparing three treatment and use an
independent-measures ANOVA to evaluate the mean
differences and then compute η 2 . You should find
that the F is no longer significant and η 2 is relatively
small. (Note that most of the calculations were completed
in Problem 20.)
22. One of the primary advantages of a repeated-measures
design, compared to independent-measures, is that it
reduces the overall variability by removing variance
caused by individual differences. The following data
are from a research study comparing three treatment
conditions.
a. Assume that the data are from an independentmeasures
study using three separate samples, each
with n = 6 participants. Ignore the column of
P totals and use an independent-measures ANOVA
with α = .05 to test the significance of the mean
differences.
b. Now assume that the data are from a repeatedmeasures
study using the same sample of n = 6
participants in all three treatment conditions. Use
a repeated-measures ANOVA with α = .05 to test
the significance of the mean differences.
c. Explain why the two analyses lead to different
conclusions.
Treatment
1
Treatment
2
Treatment
3 P
6 9 12 27
8 8 8 24 N = 18
5 7 9 21 G = 108
0 4 8 12 ΣX 2 = 800
2 3 4 9
3 5 7 15
M = 4 M = 6 M = 8
T = 24 T = 36 T = 48
SS = 42 SS = 28 SS = 34