A team of physicians, psychiatrists, and psychologists investigated whether depressed patients exhibit more or fewer personality disorder symptoms than non depressed patients in the American Journal of Psychiatry (May 2010). A study group of over 400 psychiatric patients was monitored over a six-year period. At the start of the study, each was diagnosed as having (1) major depression only, (2) personality disorder only, or (3) both major depression and personality disorder. Of interest to the researchers was the number of personality disorder criteria met at the end of the study. Consider a regression model for the number of personality disorders (y).
a. Write a model for E(y) as a function of the qualitative variable, patient diagnosis group.
b. If there are no differences among the mean number of personality disorders for the three patient groups, what are the values of the b's in the model, part a?
c. How could you test to determine if the mean number of personality disorders for the major depression-only patients is less than the corresponding mean for the patients with both major depression and personality disorder?