A Power Formula for the Mantel-Haenszel Test for Differential Item Functioning

• In Event: Detecting and Explaining Differential Item Functioning

Abstract

In this paper we derive a power formula of the Mantel-Haenszel (MH) test for the differential item functioning (DIF). The formula describes the behavior of the power when the number of items is large so that the measured latent trait can be considered as the matching variable in the MH test. As shown in the derived formula, the asymptotic power is related to the sample size, effect size of DIF, the item response function (IRF) and the distribution of the latent trait of the reference and the focal groups. It also gives analytical explanations of the behaviors of the MH test as observed in previous simulation studies. The formula for sample size calculation is also derived.

Author

• Zhushan Mandy Li, Boston College