8.10 A case–control study has eight 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

“low” or “high.” For three pairs, both the case and the control were high; for one pair, both the case and the control were low; for three pairs, the case was high and the control was low; for one pair, the case was low and the control was high.

a. Display the data in a 2 × 2 cross-classification of diet for the case against diet for the control. Display the 2 × 2 × 8 table with partial tables relating diet to response (case, control) for the matched pairs. Successive parts refer to these as Table A and Table B.

b. Find the McNemar z2 statistic for Table A and the CMH statistic (4.9) for Table B. Compare.

c. For Table B, show that the CMH statistic does not change if you delete pairs from the data set in which both the case and the control had the same diet.

d. This sample size is too small for these large-sample tests. Find the exact Pvalue for testing marginal homogeneity against the alternative hypothesis of a higher incidence of colon cancer for the “high” red meat diet. (See Problem 8.5.)