Chapter 13, Problem 19P

In Problem 18 the data show large and consistent differences between subjects. For example, subject A has the largest score in every treatment and subject D always has the smallest score. In the second stage of the ANOVA. the large individual differences get subtracted out of the denominator of the F-ratio. which results in a larger value for F.

The following data were created by using the same numbers that appeared in Problem 18. I1oever. we eliminated the consistent individual differences by scrambling the scores within each treatment.

		Treatment
Subject	I	II	III	P
A	6	2	3	11	$G=48$
B	5	1	5	11	${\displaystyle \sum X^2}=294$
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 $\alpha =.05$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.

The following data were obtained from a repeated- measures study comparing three treatment conditions.

		Treatment
Subject	I	II	III	P
A	6	8	10	24	$G=48$
B	5	5	5	15	${\displaystyle \sum X^2}=294$
C	1	2	3	6
D	0	1	2	3
	$T=12$	$T=16$	$T=20$
	$SS=26$	$SS=30$	$SS=38$

Use a repeated-measures ANOVA with $\alpha =.05$ to determine whether these data are sufficient to demonstrate significant differences between the treatments.