Chapter 13, Problem 21P

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 ${\eta }^2$ . Assume that the same data were obtained from an independent- measures study comparing three treatment and use an independent measures ANOVA to evaluate the mean differences and then compute ${\eta }^2$ . You should find that the F is no longer significant and ${\eta }^2$ is relatively small. (Note that most of the calculations were completed in Problem 20.)

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	${\displaystyle \sum X^2}=400$
E	0	1	2	3
F	2	3	4	9
	$T=18$	$T=24$	$T=30$
	$SS=28$	$SS=32$	$SS=40$

a. Use a repeated-measures ANOVA with $\alpha =.05$ to determine whether the mean number of steps changes significantly from one week to another.

b. Compute ${\eta }^2$ 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.