Psy 612
Winter 2005
Midterm
Examination
General instructions: Exams are due in class by 10:00 AM on Thursday, February 10. Report your results appropriately. Do not hand in “raw” computer output (but you may cut and paste when appropriate). You may use any non-human resource available to you. For the purpose of this examination, professors, graduate students, undergraduates, and your fellow classmates are to be considered human. Please direct any questions about the examination to the instructor or teaching assistants for this course (even though they are only human). Don’t suffer in silence. Let us make the decisions about whether we can ethically answer your questions.
1. A marital researcher is interested in comparing the effects of two different treatments for distressed couples. She randomly assigns distressed couples to one of two therapies. Couples assigned to the first "talking" therapy are encouraged to share their feelings and to discuss the issues confronting them. Couples assigned to the second "doing" therapy are encouraged to do pleasant things with each other and not to focus on their problems. Every month, the couples are brought into the laboratory and their interactions during a problem-solving task are coded. Higher scores indicate more positive affect. The researcher predicts that couples engaged in the "doing" therapy will show more positive affect at the conclusion of the 4 months and that their relationships will improve at a faster rate than couples engaged in the "talking" therapy.
a. Write out the structural model for these data; use S=subject couples, T=therapy, M=month. Treat time as fixed.
b. Write out the expected mean square table. Be sure to identify the correct error term for each effect. Calculate the degrees of freedom for each effect. Identify the correct degrees of freedom for each F ratio. If a quasi-F ratio is required, specify the terms that would contribute to the numerator and denominator of the ratio and write out the formulas for the degrees of freedom specifying the MS that would be used.
c. Conduct a standard analysis that corresponds to your E(MS) table.
d. Test the hypothesis that at the conclusion of the 4 months of therapy that the couples who had the “doing” therapy will show more positive affect than the couples who had the “talking” therapy.
e. Test the hypothesis that the rate of improvement for couples engaged in the “doing” therapy was greater than the rate of improvement for couples engaged in the “talking” therapy.
f. Plot the means for the therapy X time interaction.
g. Interpret your results.
2. A researcher has been hired to test the relative effectiveness of two different strategies for coping with the deleterious effects of situational anxiety on task performance. The first strategy (Cognitive) requires that the subject cognitively reinterpret the stressful situation and thereby alter the experienced affect. The second strategy (Emotional) requires that the subject induce a positive emotional response that is incompatible with the anxiety. To test these strategies, the researcher recruits 90 subjects and randomly assigns them to one of three conditions: No intervention (control), Cognitive strategy, and Emotional strategy. The subjects assigned to each condition are then trained in the use of the appropriate strategies in small groups of 6 participants each (the control subjects receive a “placebo” training program). Each subject is then run individually through the experimental procedure. In this procedure, the subject is asked to perform a cognitively demanding task under stress and under a no-stress condition. Higher numbers indicate better performance. Negative values are possible. The researcher expects that no training will be able to completely erase the effects of stress. Hence she hypothesizes that performance will degrade under stress for all groups. She also hypothesizes that both amelioration procedures will produce better performance under stress than the control training and that the cognitive procedure will be superior to both the control training and the emotional procedure.
a. Write out the structural model for this design; use S=subjects, G=group, T=training, and C=condition.
b. Write out the expected mean square table. Be sure to identify the correct error term for each effect. Calculate the degrees of freedom for each effect. Identify the correct degrees of freedom for each F ratio. If a quasi-F ratio is required, specify the terms that would contribute to the numerator and denominator of the ratio and write out the formulas for the degrees of freedom specifying the MS that would be used.
c. Conduct a standard analysis that corresponds to your E(MS) table.
d. Test the following hypotheses (HINT: there is more than one way to do this!)
1. Test whether there was an overall decrease in performance under stress.
2. Test whether there were differences between training conditions in the no stress condition.
3. For each of the training conditions, test whether there was a decrease in performance under stress.
4. Test whether the decrease in performance under stress (from the performance observed without stress) in the control condition was greater than the decrease in performance observed in the other two conditions.
5. Test whether the decrease in performance under stress (from the performance observed without stress) in the cognitive condition was greater than the decrease in performance observed in the emotion condition.
6. Are you concerned about the number of tests you have conducted? If you were, what would you do?
e. Interpret your results.
3. While waiting for you to analyze her data, the researcher in problem 2 decides to design a follow-up study to determine whether the results would generalize. So, she replicates the study in problem 2 but this time each subject works under only one condition -- stress or no-stress. This time, she recruits 180 subjects and then randomly assigns them to work under stress or no stress. Then 1/3 of each group is assigned to the control, emotional, or cognitive training conditions. The subjects in each of these conditions are further divided into 6 person groups for training.
a. Write out the structural model for this design; use S=subjects, G=group, T=training, and C=condition.
b. Write out the expected mean square table. Be sure to identify the correct error term for each effect. Calculate the degrees of freedom for each effect. Identify the correct degrees of freedom for each F ratio. If a quasi-F ratio is required, specify the terms that would contribute to the numerator and denominator of the ratio and write out the formulas for the degrees of freedom specifying the MS that would be used.
|
Therapy |
Month 1 |
Month 2 |
Month 3 |
Month 4 |
|
Talk |
6 |
4 |
11 |
5 |
|
Talk |
9 |
7 |
7 |
6 |
|
Talk |
8 |
5 |
11 |
10 |
|
Talk |
3 |
2 |
4 |
8 |
|
Talk |
6 |
8 |
6 |
3 |
|
Talk |
3 |
4 |
10 |
3 |
|
Talk |
3 |
5 |
8 |
4 |
|
Talk |
3 |
3 |
8 |
3 |
|
Talk |
6 |
9 |
5 |
9 |
|
Talk |
6 |
7 |
10 |
8 |
|
Talk |
1 |
8 |
3 |
5 |
|
Talk |
5 |
9 |
6 |
7 |
|
Talk |
1 |
6 |
10 |
11 |
|
Talk |
4 |
9 |
7 |
9 |
|
Talk |
4 |
9 |
5 |
7 |
|
Do |
7 |
11 |
5 |
5 |
|
Do |
2 |
9 |
4 |
5 |
|
Do |
0 |
3 |
9 |
6 |
|
Do |
0 |
6 |
12 |
12 |
|
Do |
9 |
11 |
10 |
7 |
|
Do |
0 |
10 |
5 |
10 |
|
Do |
5 |
5 |
9 |
8 |
|
Do |
10 |
2 |
4 |
9 |
|
Do |
3 |
2 |
8 |
13 |
|
Do |
3 |
11 |
11 |
11 |
|
Do |
1 |
5 |
8 |
15 |
|
Do |
0 |
2 |
12 |
14 |
|
Do |
2 |
1 |
13 |
10 |
|
Do |
9 |
3 |
10 |
9 |
|
Do |
6 |
5 |
3 |
13 |
|
Training |
Group |
Stress |
No Stress |
|
Cognitive |
1 |
3 |
8 |
|
Cognitive |
1 |
4 |
6 |
|
Cognitive |
1 |
7 |
8 |
|
Cognitive |
1 |
3 |
2 |
|
Cognitive |
1 |
1 |
8 |
|
Cognitive |
1 |
0 |
4 |
|
Cognitive |
2 |
1 |
1 |
|
Cognitive |
2 |
9 |
4 |
|
Cognitive |
2 |
6 |
9 |
|
Cognitive |
2 |
2 |
6 |
|
Cognitive |
2 |
3 |
5 |
|
Cognitive |
2 |
3 |
6 |
|
Cognitive |
3 |
9 |
0 |
|
Cognitive |
3 |
4 |
2 |
|
Cognitive |
3 |
6 |
9 |
|
Cognitive |
3 |
3 |
6 |
|
Cognitive |
3 |
2 |
0 |
|
Cognitive |
3 |
8 |
2 |
|
Cognitive |
4 |
3 |
4 |
|
Cognitive |
4 |
0 |
1 |
|
Cognitive |
4 |
9 |
4 |
|
Cognitive |
4 |
2 |
8 |
|
Cognitive |
4 |
5 |
3 |
|
Cognitive |
4 |
4 |
8 |
|
Cognitive |
5 |
8 |
1 |
|
Cognitive |
5 |
5 |
8 |
|
Cognitive |
5 |
2 |
2 |
|
Cognitive |
5 |
6 |
8 |
|
Cognitive |
5 |
8 |
3 |
|
Cognitive |
5 |
0 |
6 |
|
Emotional |
6 |
5 |
4 |
|
Emotional |
6 |
7 |
8 |
|
Emotional |
6 |
4 |
8 |
|
Emotional |
6 |
0 |
9 |
|
Emotional |
6 |
6 |
6 |
|
Emotional |
6 |
3 |
6 |
|
Emotional |
7 |
7 |
5 |
|
Emotional |
7 |
7 |
3 |
|
Emotional |
7 |
5 |
9 |
|
Emotional |
7 |
0 |
3 |
|
Emotional |
7 |
2 |
8 |
|
Emotional |
7 |
0 |
6 |
|
Emotional |
8 |
5 |
0 |
|
Emotional |
8 |
7 |
4 |
|
Emotional |
8 |
0 |
5 |
|
Emotional |
8 |
4 |
0 |
|
Emotional |
8 |
0 |
1 |
|
Emotional |
8 |
7 |
9 |
|
Emotional |
9 |
1 |
6 |
|
Emotional |
9 |
3 |
4 |
|
Emotional |
9 |
7 |
6 |
|
Emotional |
9 |
-1 |
7 |
|
Emotional |
9 |
0 |
0 |
|
Emotional |
9 |
3 |
9 |
|
Emotional |
10 |
3 |
8 |
|
Emotional |
10 |
3 |
6 |
|
Emotional |
10 |
6 |
0 |
|
Emotional |
10 |
0 |
3 |
|
Emotional |
10 |
2 |
0 |
|
Emotional |
10 |
0 |
2 |
|
Control |
11 |
6 |
3 |
|
Control |
11 |
2 |
0 |
|
Control |
11 |
1 |
8 |
|
Control |
11 |
0 |
2 |
|
Control |
11 |
-2 |
4 |
|
Control |
11 |
0 |
5 |
|
Control |
12 |
1 |
6 |
|
Control |
12 |
1 |
8 |
|
Control |
12 |
1 |
1 |
|
Control |
12 |
5 |
9 |
|
Control |
12 |
4 |
2 |
|
Control |
12 |
5 |
5 |
|
Control |
13 |
3 |
2 |
|
Control |
13 |
3 |
4 |
|
Control |
13 |
2 |
7 |
|
Control |
13 |
2 |
7 |
|
Control |
13 |
1 |
3 |
|
Control |
13 |
2 |
6 |
|
Control |
14 |
0 |
7 |
|
Control |
14 |
6 |
4 |
|
Control |
14 |
3 |
7 |
|
Control |
14 |
3 |
3 |
|
Control |
14 |
0 |
7 |
|
Control |
14 |
6 |
2 |
|
Control |
15 |
-2 |
9 |
|
Control |
15 |
3 |
4 |
|
Control |
15 |
-1 |
3 |
|
Control |
15 |
4 |
9 |
|
Control |
15 |
-1 |
9 |
|
Control |
15 |
0 |
6 |