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The Mantel-Haenszel (MH) approach of Holland and Thayer is frequently used to assess differential item functioning (DIE). The formula for the variance of the MH DIE statistic is based on work by Phillips and Holland, and Robins, Breslow, and Greenland. Recent simulation studies showed that, for a given sample size, the MH variances tended to be larger when items were administered to "examinees" who were randomly selected from a population than when items were administered adaptively. An analytic perspective shed some light on this result. Although the general form of the MH variance is complex and does not provide an intuitive understanding of the phenomenon, application of certain Rasch model assumptions yields a simple expression that appears to explain the difference in variances for adaptive versus nonadaptive administration. The results suggest that adaptive testing may lead to more efficient application of MH DIF analyses.
Rebecca Zwick (Sun,) studied this question.