8.8 A crossover experiment with 100 subjects compares two treatments for migraine headaches. The response scale is success (+) or failure (−). Half the study subjects, randomly selected, used drug A the first time they got a migraine headache and drug B the next time. For them, six had responses

(A+,B+), 25 had responses (A+,B−), 10 had responses (A−,B+), and nine had responses (A−,B−). The other 50 subjects took the drugs in the reverse order. For them, 10 were (A+,B+), 20 were (A+,B−), 12 were

(A−,B+), and eight were (A−,B−).

a. Ignoring treatment order, use the McNemar test to compare the success probabilities for the two treatments. Interpret.

b. The McNemar test uses only the pairs of responses that differ. For this study, Table 8.11 shows such data from both treatment orders. Explain why a test of independence for this table tests the hypothesis that success rates are identical for the two treatments. Analyze these data, and interpret.