Performance of the Mantel-Haenszel and Simultaneous Item Bias Procedures for Detecting Differential Item Functioning

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Abstract
Two nonparametric procedures for detecting differ ential item functioning (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 reference groups, pro portion of DIF items in the test, DIF effect sizes, and type of item. 1,296 conditions were studied. The SIB and MH procedures were equally powerful in detecting uniform DIF for equal ability distributions. The SIB procedure was more powerful than the MH procedure in detecting DIF for unequal ability distributions. Both procedures 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 SIB procedure but did affect the MH procedure. This is important because ability distribu tion differences between two groups often are found in practice. The Type I error rates for the MH statistic were well within the nominal limits, whereas they were slightly higher than expected for the SIB statistic. Com parisons between the detection rates of the two proce dures were made with respect to the various factors. Index terms: differential item functioning, Mantel- Haenszel statistic, power, simultaneous item bias statis tic, SIBTEST, Type I error rates.