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The aim of the current study was to compare the effectiveness of the DIFT and SIBTEST methods in detecting measurement invariance for tests according to sample size and differences in ability distribution. A factorial experimental design was used to look at how the detection method, sample size, and differences in ability distribution all affect each other. Examining type I error rates and test power served to accomplish this. Two studies were conducted, the first to examine Type I error rates and the second to examine test power while controlling for ability distribution differences and sample size. Data were analyzed using statistical methods for each detection method to test the null hypothesis of no differential performance and obtain Type I error rates and test power. The data were processed using mixed-variance analysis. Based on the results of the statistical analysis, a number of important findings were obtained, including: both the SIBTEST and DIFT methods were effective in detecting differential performance of the test in general; the differential item functioning (DIF) method was more effective than the simultaneous item bias test (SIBTEST) when considering sample sizes of 1000 or more. And the differential item bias test was more effective in detecting differential performance of items and tests in the absence of ability distribution differences. However, in the presence of ability distribution differences, both methods were ineffective, as DIFT suffered from low statistical power and SIBTEST suffered from inflated Type I error rates. Therefore, the study recommends using both methods together to detect differential test performance in the presence of ability distribution differences between groups.