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For an observational study to compare two groups with respect to a dichotomous outcome variable, the design strategy of matching observational units with respect to a potential confounding variable X is compared with the strategy of selecting independent samples with possible poststratification on X for bias control. The comparison is based on asymptotic relative efficiencies of appropriate Mantel—Haenszel chi-squared tests. It is found that proper understanding requires that the prospective and the retrospective study designs be separately considered, and that in certain circumstances the effect of matching on design efficiency is entirely different for the two designs. Conditions are established under which matching is more efficient than poststratification for the control of confounding.
Myra L. Samuels (Thu,) studied this question.