ABSTRACT
We all know that, when using test score as a matching variable with a Mantel- Haenszel analysis for differential item functioning (DIF), the item under study should be included. But do we know why? Holland and Thayer (1988) proved this result for items following the Rasch model, and Zwick (1990) established the degree of its applicability for more general item response models. In her discussion, Zwick illustrated the appropriateness of the total test score as a matching variable for the binomial test model (which may be thought of as a special case of the Rasch model with all items of equal difficulty). It is this illustration that I would like to review and develop here (generally following her notation). My motivation for doing this is that the binomial model is both simple and familiar, so that it may help improve our intuitions regarding the role of a matching variable in DIF analyses.
