The Mantel‐Haenszel procedure is a noniterative contingency table method for estimating and testing a common two‐factor association parameter in a 2×2×k table. As such it may be used to study “item bias” or differential item functioning in two groups of examinees. This technique is discussed in this context and compared to other related techniques as well as to item response theory methods.

No abstract

factor analysis, EM algorithms, maximum likelihood,

We developed an empirical Bayes (EB) enhancement to Mantel‐Haenszel (MH) DIF analysis in which we assume that the MH statistics are normally distributed and that the prior distribution of underlying DIF parameters is also normal. We use the posterior distribution of DIF parameters to make inferences about the item's true DIF status and the posterior predictive distribution to predict the item's future observed status. DIF status is expressed in terms of the probabilities associated with each of the five DIF levels defined by the ETS classification system: C–, B–, A, B+, and C+. The EB methods yield more stable DIF estimates than do conventional methods, especially in small samples, which is advantageous in computer‐adaptive testing. The EB approach may also convey information about DIF stability in a more useful way by representing the state of knowledge about an item's DIF status as probabilistic.