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chap9 - Chapter 9 Adjusting for a Factor 9.1 Study...

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Chapter 9 Adjusting for a Factor 9.1 Study Suggestions Simpson’s paradox and standardized rates constitute a nice completion to the argument, begun in Chap- ter 7, that it is difficult to interpret the findings of an observational study. The real importance of Simpson’s paradox rests in the following realization. The 2 × 2 table of any ob- servational study can be viewed as a ‘collapsed’ ta- ble. The researcher must always remember that there could exist a meaningful factor for which ‘uncollaps- ing’ the table would result in a reversal of the di- rection of the relationship between the response and populations. The main problem my students have with Simp- son’s paradox and standardized rates is in keeping the roles of the three variables straight. There is a response, there is a variable, that defines the pop- ulations to be compared, and there is a factor that may influence the response. For example, for the data on page 295 of the text, the response is the at- titude toward drinking and driving. The populations consist of female and male drivers. Finally, it was conjectured that drinking frequency would influence response, so the factor was taken to be drinking fre- quency. Simpson’s paradox can occur, and standardized rates will yield interesting insight, only if the factor is strongly related (statistically) to both the popula- tion and the response. For example, if women and men had the same distribution of drinking frequen- cies then computing the standardized rates would be a waste of time. (If men and women have the same weights, the standardized rate would equal the orig- inal rate, since there would be no effect of replacing the women’s weights with the men’s weights, or vice versa, since the weights are identical.) Moreover, if attitude were not related to drinking frequency, then the proportion of successes, for either gender, would be the same in each drinking frequency cate- gory. Thus, the weights used would have no impact, since we would be computing weighted averages of identical numbers. If you use the Mantel-Haenszel test to analyze data from an observational study, remember that there is not necessarily a single correct analysis strategy. Consider, for example, the study of how attitude to- wards drinking and driving depends on gender that is analyzed in the text in Chapter 9. If a researcher simply wants to compare females and males there is no need to consider using the techniques discussed in Chapter 9. If, however, the researcher wants to in-

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chap9 - Chapter 9 Adjusting for a Factor 9.1 Study...

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