An experiment was conducted to evaluate the use of three drugs in the treatment of leprosy. Ten patients were randomized to each of the three drug treatments. For each patient, six sites on the body at which Leprosy bacilli tended to congregate were selected. At these sites, a score representing the average abundance of L. bacilli was obtained before the experiment begins. Consider these initial abundances as values of covariate. A similar score is obtained after several months of treatment. Drugs A and B are antibiotics, while drug C is an inert drug included as a control. .
a. What linear model do you propose to use? Give a complete description of the model.Show how to set up the appropriate "X” matrix for this model.
b. Given that the goal is to test for differences among the drugs, explain exactly how your proposed model will help in this regard.
c. Assume you obtain the estimated solution β to the linear model using the X matrix for the model you specified above. Give the k’ vector you would use to compute the difference between two adjusted treatment means.
d. Write down the expression you would use to compute the standard error of the difference computed in part c.
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