Testing Features of Graphical DIF: Application of a Regression Correction to Three Nonparametric Statistical Tests

Abstract

Inspection of differential item functioning (DIF) in translated test items can be informed by graphical comparisons of item response functions (IRFs) across translated forms. Due to the many forms of DIF that can emerge in such analyses, it is important to develop statistical tests that can confirm various characteristics of DIF when present. Traditional nonparametric tests of DIF (Mantel‐Haenszel, SIBTEST) are not designed to test for the presence of nonuniform or local DIF, while common probability difference (P‐DIF) tests (e.g., SIBTEST) do not optimize power in testing for uniform DIF, and thus may be less useful in the context of graphical DIF analyses. In this article, modifications of three alternative nonparametric statistical tests for DIF, Fisher's χ 2 test, Cochran's Z test, and Goodman's U test (Marascuilo & Slaughter, 1981), are investigated for these purposes. A simulation study demonstrates the effectiveness of a regression correction procedure in improving the statistical performance of the tests when using an internal test score as the matching criterion. Simulation power and real data analyses demonstrate the unique information provided by these alternative methods compared to SIBTEST and Mantel‐Haenszel in confirming various forms of DIF in translated tests.