The books Web site (wvvw.stat.ufl.edu/ ¼aa/cda/cda.html) has a 3 Ã 4 Ã 4 table that cross-classifies dumping

The book€™s Web site (wvvw.stat.ufl.edu/ ˆ¼aa/cda/cda.html) has a 3 × 4 × 4 table that cross-classifies dumping severity (Y) and operation (X) for four hospitals (H). The four operations refer to treatments for duodenal ulcer patients and have a natural ordering. Dumping severity describes a possible undesirable side effect of the operation. Its three categories are also ordered.

a. Table 7.22 shows results of generalized CMH tests. Interpret, explaining how one test can be much more significant than the others.

b. Let {x_i = i}. Fit the model logit[P(Y ‰¤ j | H = h, X = i)] = α_j + µ_h + βx_i. Test conditional independence of X and Y using it, and interpret β̂. Which generalized CMH test has the same spirit as this?

c. Does an improved fit result from allowing the operation effect to vary by hospital? Interpret.

Table 7.22:

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Summary Statistics for dumping by operate Controlling for hospital Alternative Hypothesis DF Value Statistic Prob Nonzero Correlation 6.3404 0.0118 Row Mean Scores Differ General Association 0.0862 0.1016 6.5901 10.5983