7.6 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.

a. Fit the homogenous association model using all departments, test whether its fit is significantly worse than that of the saturated model, report the results, and state the conclusions.

b. Is the test performed in part

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

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

c. Obtain the standardized residuals for the homogenous association model and discuss whether the largest residuals (lack of fit) tend to correspond to certain departments.

If so, which departments are these, and what does this indicate?