Use odds ratios in Table 8.3 to illustrate the collapsibility conditions.

a. For (A, C, M), all conditional odds ratios equal 1.0. Explain why all reported marginal odds ratios equal 1.0.

b. For (AC, M), explain why (i) all conditional odds ratios are the same as the marginal odds ratios, and (ii) all µÌ‚_ac+ = n_ac+.

c. For (AM, CM), explain why (i) the AC conditional odds ratios of 1.0 need not be the same as the AC marginal odds ratio, (ii) the AM and CM conditional odds ratios are the same as the marginal odds ratios, and (iii) all µÌ‚_a+m = n_a+m and µÌ‚_+cm = n_+cm.

d. For (AC, AM, CM), explain why (i) no conditional odds ratios need be the same as the related marginal odds ratios, and (ii) the fitted marginal odds ratios must equal the sample marginal odds ratios.

Table 8.3:

Alcohol, Cigarette, and Marijuana Use for High School Seniors Marijuana Use Alcohol Cigarette Use Use Yes No Yes Yes 911 538 No 44 456 No Yes 3 43 No 2 279