Item purification does not always improve DIF detection: a counter-example with Angoff’s Delta plot

Item purification is an iterative process that is often advocated as improving the identification of items affected by differential item functioning (DIF). With test-score based DIF detection methods, item purification iteratively removes the items currently flagged as DIF from the test scores in order to get purified sets of items, unaffected by DIF. The purpose of this paper is to highlight that item purification is not always useful and that a single run of the DIF method may return equally suitable results. Angoff’s Delta plot is considered as a counter-example DIF method, with a recent improvement to the derivation of the classification threshold. Several possible item purification processes may be defined with this method, and all of them are compared through a simulation study and a real data set analysis. It appears that none of these purification processes clearly improves the Delta plot performance. A tentative explanation is drawn from the conceptual difference between the modified Delta plot and the other traditional DIF methods.