Angoff's delta method revisited: Improving DIF detection under small samples

Most methods for detecting differential item functioning (DIF) are suitable when the sample sizes are sufficiently large to validate the null statistical distributions. There is no guarantee, however, that they will still perform adequately when there are few respondents in the focal group or in both the reference and the focal group. Angoff's delta plot is a potentially useful alternative for small-sample DIF investigation, but it suffers from an improper DIF flagging criterion. The purpose of this paper is to improve this classification rule under mild statistical assumptions. This improvement yields a modified delta plot with an adjusted DIF flagging criterion for small samples. A simulation study was conducted to compare the modified delta plot with both the classical delta plot approach and the Mantel–Haenszel method. It is concluded that the modified delta plot is consistently less conservative and more powerful than the usual delta plot, and is also less conservative and more powerful than the Mantel–Haenszel method as long as at least one group of respondents is small.