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STATISTICS 402 - Assignment 7 Due April 15, 2011 1. An experiment was done with patients suffering from agoraphobia (the fear of going out in public places). There are three factors of interest; drug (a selective serotonin reuptake inhibitor (SSRI) e.g. Prozac, a tricyclic antidepressant e.g. Elavil, an antianxiety e.g. Xanax and Placebo – offered as a new drug for agoraphobia), type of psychotherapy (psychodynamic, cognitive/behavioral, and group), and depression (yes/no). The experimenters were able to assign the 12 combinations of the drug and type of psychotherapy to 3 depressed and 3 non-depressed agoraphobics. After 6 months the severity of agoraphobia was measured for each subject (maximum score 30, minimum score 0). The data are given below and are also available in a JMP data table available on the course web page. Not Depressed Psychodynamic Depressed Not Depressed Cognitive Behavioral Depressed Not Depressed Group Depressed Prozac 11 12 7 10 8 8 8 9 11 9 12 10 14 11 10 12 9 8 Elavil 13 10 11 11 7 8 10 11 12 13 13 16 15 13 11 11 11 14 Xanax 18 19 20 16 14 13 12 13 11 8 10 12 20 19 19 16 17 18 Placebo 21 24 21 18 18 21 19 16 16 17 16 15 11 13 15 10 10 13 a) What are the response, conditions and experimental material? b) How do you know that this experiment was run as a completely randomized design? c) The severity of agoraphobia for each participant at the beginning of the study will vary. Where will this variation end up in the analysis of the data? Explain briefly. d) Use JMP to calculate means for each of the factors and display these means in appropriate plots. What factors appear to have effects on the response? Explain briefly. e) Are there statistically significant differences among the 24 treatment sample means? Report the appropriate F ratio, P-value, decision and reason for the decision. 1 f) What factors are statistically significant? For each significant factor report the F ratio and P-value. g) What interactions are statistically significant? For each significant interaction report the F ratio and P-value. h) Use JMP to calculate means for the combinations of factors taken two-at-a-time and display these in interaction plots. You should have three interaction plots. Describe each interaction plot and indicate how your description matches the results of the tests conducted in g). i) Based on the analysis above, what statistically valid recommendations for treatment of agoraphobia can be made? j) You should turn in the following JMP output. If additional output is turned in, I will deduct points. Factor level means and plots. A complete analysis of variance table showing sources of variability: Model, Error and C. Total. Effect tests for all factors and interactions. Means for the combinations of factors taken two-at-a-time and 2-way interaction plots. 2. The maker of Prozac makes the claim that for depressed patients receiving Cognitive/Behavioral, Group or Psychodynamic therapy taking Prozac will result in a lower mean severity score than Placebo and the difference in mean severity scores is statistically significant. The FDA makes the counter claim that for some depressed patients receiving therapy taking Placebo is just as effective, on average, as taking Prozac. Analyze a subset of the data, just depressed patients taking either Prozac or Placebo, to see whose claim is supported by the data. For each claim provide, and explain, statistical evidence either for or against the claim. 2