7.7 In Chapter 5 (Section 5.6), we discussed the Berkeley graduate admissions data, where the variables of interest involved the applicant’s sex and admission to graduate school across six departments. The data are presented in Table 5.10 and can be analyzed using log-linear models. Remove Department A from the data set and fit log-linear models to the data on the remaining departments.

a. Fit the homogenous association model to the data set without Department A, test whether its fit is significantly worse than that of the saturated model, report the results, and state the conclusions.

b. Fit the conditional independence model where gender and admission are conditionally independent (given department) to the data set without Department A. Test whether this model fits significantly worse than the homogenous association model, report the results, and state the conclusions.

c. Is the test performed in part

(b) analogous to the Breslow–Day or the Cochran–

Mantel–Haenszel (CMH) test, which were discussed in Chapter 5? Explain.