Question: In a small clinical trial, 10 patients with chronic pain were randomly assigned to receive either drug A or drug B for one month. After completing the month, they then had a two week “wash-out” period during which no drug was taken, and then received the alternative drug for one month. At the end of the study, they were asked to state which drug they preferred because it gave them greater relief from the pain. Each patient had to choose one drug. Eight patients said that they preferred drug A.

a) If drug A and drug B were truly equal in their effects in reducing pain, what would be the probability that a patient expressed a preference for drug A over drug B?

b) How many ways are there of obtaining 10 patients expressing a preference for drug A. Repeat for 9 patients, 8 patients,…1, 0 patients. Tabulate your results.

c) What is the probability of having 8 patients express a preference for drug A if drugs A and B were truly equal in their effects? What is the probability of having 8 or more patients express a preference for drug A under the same condition? Show how these probabilities can be obtained from your table in part b)

d) Draw conclusions with regard to the finding that 8 patients preferred drug A. Give assumptions you have made in carrying out the above calculations and discuss their appropriateness.