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# ansfin2000 - Final Exam December 2000 ANSWERS Categorical...

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Final Exam, December 2000, ANSWERS Categorical Data Analysis for Epidemiologic Studies, CHL5407H 1a. Adoption of a Pearson chi-square test is reasonable. Only the degrees of freedom are in question. The Pearson chi-square test should be calculated using two degrees of freedom since there are no observations, and hence no information, in the row reserved for subjects with severely impaired lung function. The expected number of observations in these two cells is zero. How could these cells even be used to calculate the Pearson chi-square test given by χ 2 P = ∑ ∑ ( O - E ) 2 /E ? The expected numbers of observations in all other cells are sufficiently large to support the use of a Pearson chi-square test with two degrees of freedom. 1b. Several different methods of analysis could be used 1. Fisher’s exact test is applicable to analysis of data from an r × c contingency table and so could be used to test for an association between smoking status and lung function. Adoption of this test would still require omitting the row reserved for subjects with severely impaired lung function. One advan- tage of an exact test is that it is valid regardless of the sample size. One disadvantage is that Fisher’s exact test may be overly conservative relative to Pearson’s chi-square test if the large sample requirements of the latter procedure are satisfied. If concerned that Fisher’s exact test might not be applicable to analysis of data from an 3 × 2 contingency table one could col- lapse lung function into two categories. For example, employees could be classified as either having normal lung function or as having borderline or worse than borderline lung function. Now however one is omitting consid- eration for differences in smoking status between employees with borderline lung function and employees whose lung function is moderately impaired. The row reserved for subjects with severely impaired lung function must still be omitted.

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