Chapter 11, Problem 21P

The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit only occurs if the individual difference are consistent across treatment conditions. In Problem 20, for example, the participants with the highest scores in the neutral-word condition also had the highest scores in the swear-word condition. Similarly, participants with the lowest scores in the first condition also had the lowest scores in the second condition. To construct the following data, we started with the scores in Problem 20 and scrambled the scores in Treatment 2 to eliminate the consistency of the individual differences.

Participant	Neutral Word	Swearing
A	9	5
B	9	2
C	9	5
D	4	10
E	10	8
F	9	4
G	6	7
H	10	5
I	6	8

a. If the data were from an independent-measures study using two separate samples, each with n = 9 participants, what value would be obtained for the independent-measures t statistic. Note: The scores in each treatment, the sample means, and the SS values are the same as in Problem 20. Nothing has changed. With α – .05, is there a significant differ­ence between the two treatment conditions?

b. Now assume that the data are from a repeated-measures study using the same sample of n = 9 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repealed-measures t statistic. Using α = .05, is there a significant difference between the two sets of scores? (Because there no longer are consistent individual differences you should find that the repeated-measures t no longer reduces the variance.)