Question

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 differences are consistent across treatment conditions. In problem 21, for example, the participants with the highest scores in the more-sleep condition also had the highest scores in the less-sleep 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 21 and scrambled the scores in treatment 1 to eliminate the consistency of the individual differences.

Number of Academic Problems

Student                  Above Average Sleep          Below Average Sleep

A                                             10                                            13

B                                              8                                              14

C                                              5                                              13

D                                             5                                              5

E                                              4                                              9

F                                              10                                            6

G                                             11                                            6

H                                             3                                              6

a. Treat the data as if the scores are from an independent-measures study using two separate samples, each with n = 8 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? Note: The scores in each treatment are the same as in Problem 21. Nothing has changed.

b. Now assume that the data are from a repeated measures study using the same sample of n = 8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repeated-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? (You should find that removing the individual differences with a repeated-measures t no longer reduces the variance because there are no consistent individual differences.)

Answer 1

a) From the given data

(1) Define Null and Alternative Hypothesis:

H0: There is no significant difference between the two sets of scores

H1: There is significant difference between the two sets of scores

i.e.

Thus we conclude that there is no significant difference between the two sets of scores

(b) Paired 't' Test:From the given data

Thus we conclude that there is no significant difference between the two sets of scores