A team of psychologists designed a study in which 12 psychiatric patients diagnosed as having generalized anxiety disorder were randomly assigned to one of 3 new kinds of therapy, here labeled X, Y, and Z. One year after therapy, the patients' entire mental health scores were as follows:
Therapy X- 85 79 84 67
Therapy Y- 78 81 68 75
Therapy Z- 79 83 75 74
Do these results suggest that different therapies have different effects upon mental health? (Employ the .05 level.)
a. Employ the five steps of the hypothesis testing. Show all work.
b. Discuss the logic of what you've done to a person who is unfamiliar with analysis of variance.