The purpose of this study was to compare two non-parametric procedures, the Mantel-Haenszel (MH) procedure and the simultaneous item bias (SIB) procedure, with respect to their Type I error rates and power, and to investigate the conditions under which asymptotic distributional properties of the SIB and MH were obtained. Data were simulated to reflect a variety of conditions; the factors manipulated were sample sizes, ability distributions of the focal and the reference groups, percent of DIF items in the test, types of item and DIF effect sizes. Investigations of the distribution of the SIB and the MH statistics revealed that the SIB statistic had the theoretical asymptotic distributions when the sample sizes of the focal and reference groups exceeded 200, whereas the MH statistic did not have the theoretical asymptotic distributions under any condition. The MH and the SIB procedures were equally powerful in detecting DIF for equal ability distributions, and the SIB procedure was more powerful for unequal ability distributions than the MH procedure. The Type I error rates for the MH statistic were within limits, whereas they were higher for the SIB statistic than those for the MH statistic. Comparisons between the detection rates of the two procedures were made with respect to the various factors manipulated in the study. Suggestions for future research are made. (Contains 16 references and 11 tables.) (Author)