PERFORMANCE OF THE MANTEL-HAENSZEL AND SIMULTANEOUS ITEM BIAS PROCEDURES FOR DETECTING DIFFERENTIAL ITEM FUNCTIONING

Two nonparametric procedures for detecting differential item functioni ng (DIF)-the Mantel-Haenszel (MH) procedure and the simultaneous item bias (SIB) procedure-were compared with respect to their Type I error rates and power. Data were simulated to reflect conditions varying in sample size, ability distribution differences between the focal and re ference groups, proportion of DIF items in the test, DIF effect sizes, and type of item. 1,296 conditions were studied. The SIB and MH proce dures were equally powerful in detecting uniform DIF for equal ability distributions. The SIB procedure was more powerful than the MH proced ure in detecting DIF for unequal ability distributions. Both procedure s had sufficient power to detect DIF for a sample size of 300 in each group. Ability distribution did not have a significant effect on the S IB procedure but did affect the MH procedure. This is important becaus e ability distribution differences between two groups often are found in practice. The Type I error rates for the MH statistic were well wit hin the nominal limits, whereas they were slightly higher than expecte d for the SIB statistic. Comparisons between the detection rates of th e two procedures were made with respect to the various factors.