A case–control study has 8 pairs of subjects. The cases have colon cancer, and the controls are matched with the cases on gender and age. A possible explanatory variable is the extent of red meat in a subject’s diet, measured as “1 = high” or “0 = low.” The (case, control) observations on this were (1, 1) for 3 pairs, (0, 0) for 1 pair, (1, 0) for 3 pairs, and (0, 1) for 1 pair.

a. Calculate the McNemar z² for Table A and the CMH statistic for Table B. Compare.

b. This sample size is small for large-sample tests. Use the binomial distribution with Table A to find the exact P-value for testing marginal homogeneity against the alternative hypothesis of a higher incidence of colon cancer for the high-red-meat diet.