A Formulation of the Mantel-Haenszel Differential Item Functioning Parameter with Practical Implications. Statistical Report. LSAC Research Report Series.

The Mantel-Haenszel (MH) differential item functioning (DIF) parameter for uniform DIF is well defined when item responses follow the two-parameter-logistic (2PPL) item response function (IRF), but not when they follow the three-parameter-logistic (3PL) IRF, the model typically used with multiple choice items. This research report presents a general formulation of the MH DIF population parameter for any IRF and presents results for numerous 3PL uniform DIF conditions. The results indicate that for items of medium or high difficulty, the 2PL DIF parameter formulation can overestimate the 3PL DIF parameter and the MH DIF estimator may exhibit less than expected power to identify even substantial DIF in certain circumstances. Implications of this study on the routine operational task of identifying DIF at the Law School Admission Council are still not known, and may in fact be minimal. However, because some items on the Law School Admission Test (LSAT) are known to exhibit guessing behavior, the results suggest that additional research is warranted. (Contains 2 tables, 5 figures, and 13 references.) (Author/SLD)