A Different View On DIF

In this paper, we sketch our view on DIF: i.e., what it is, how it is detected, and how we deal with it when we find it. We focus on DIF in difficulty. Our start point is that DIF in difficulty can only be defined meaningfully in
terms of differences in difficulty between items. Thus, to investigate DIF, we compare the relative difficulties estimated in separate calibrations in each group. If there is DIF, it does not imply that all relative difficulties are different. Items whose relative difficulties are invariant across groups form clusters. Each cluster may be used as an anchor in a concurrent analysis and the set of anchor items or, equivalently, the set of "DIF-items", is not unique. This issue relates to what Camilli (1993) refers to as the ipsative nature of DIF and appears to be well-known among psychometricians What enticed us to bring this issue around is the observation that, when there is DIF, the relation between the latent traits in two groups depends on which set of DIF ( or anchor) items one considers. Consequently, when the purpose of the study is to equate scores on two test forms, there may be two or more equating functions that can not be distinguished with the data at hand. An explanation is offered by showing that clusters measure different latent abilities and DIF occurs because the relation between the abilities is different across groups.