Question

4) What is the modeling approach to dealing with covariates?

5) What is Simpson’s paradox?

Answer #1

(5) DEFINITION OF Simpson’s paradox

Consider three random variables *X*, *Y*, and
*Z*. Define a 2 × 2 × *K* cross-classification table
by assuming that *X* and *Y* can be coded either 0 or
1, and *Z* can be assigned values from 1 to *K*.

The marginal association between *X* and *Y* is
assessed by collapsing across or aggregating over the levels of
*Z*. The *partial association*between *X* and
*Y* controlling for *Z* is the association between
*X* and *Y* at each level of *Z* or after
adjusting for the levels of *Z*. Simpson’s paradox is said
to have occurred when the pattern of marginal association and the
pattern of partial association differ.

Various indices exist for assessing the association between two variables. For categorical variables, the odds ratio and the relative risk ratio are the two most common measures of association. Simpson’s paradox is the name applied to differences in the association between two categorical variables, regardless of how that association is measured.

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