Exact and Permutation-Based Mantel Tests for Differential Item Functioning in Dichotomous and Polytomous Items

Screens dichotomous and polytomous test items for Differential Item Functioning (DIF) using an extension of the Mantel (1963) and generalized Mantel-Haenszel statistic, with statistical significance computed via permutation rather than the conventional asymptotic chi-square approximation. Following Hemerik and Goeman (2018) , the permutation p-value is exact at the nominal level rather than an approximation, even for a finite number of permutations. This makes the test valid for small samples (fewer than 200 examinees per group), a condition common in classroom-, program-, and institution-level assessment where existing exact-inference options in other software are restricted to dichotomous items only. An optional Benjamini-Hochberg or Bonferroni correction addresses multiple comparisons when screening many items at once.