Treat the data as if the scores are from an independent-measures study using two separate samples, each with n=9 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using αα=.05 , is there a significant difference between the two sets of scores? 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 repeated-measures t statistic. Using αα=.05 , is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting H0 .)
Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of obscenities. One question, however, is whether swearing has any effect on the amount of pain that you feel. To address this issue, Stephens, Atkins, and Kingston (2009) conducted an experiment comparing swearing with other responses to pain. In the study, participants were asked to place one hand in icy cold water for as long as they could bear the pain. Half of the participants were told to repeat their favorite swear word over and over for as long as their hands were in the water. The other half repeated a neutral word. The researchers recorded how long each participant was able to tolerate the ice water. After a brief rest, the two groups switched words and repeated the ice water plunge. Thus, all the participants experienced both conditions (swearing and neutral) with half swearing on their first plunge and half on their second. The data in the following table are representative of the results obtained in the study and represented the reports of pain level of n=9 participants.
Participant
Neutral Word
Swearing
A
9
7
B
9
8
C
9
5
D
4
5
E
10
8
F
9
4
G
6
5
H
10
10
I
6
2
Treat the data as if the scores are from an independent-measures study using two separate samples, each with n=9 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using αα=.05 , is there a significant difference between the two sets of scores?
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 repeated-measures t statistic. Using αα=.05 , is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting
H0 .)
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