exactGMH - 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) <doi:10.1080/01621459.1963.10500879> and generalized Mantel-Haenszel statistic, with statistical significance computed via permutation rather than the conventional asymptotic chi-square approximation. Following Hemerik and Goeman (2018) <doi:10.1007/s11749-017-0571-1>, 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.