Validity is the most important psychometric feature that should be found in a measurement tool. Measurement equivalence is one of the evidences for the validity of measurement tools. Providing information to the researchers about the methods of identifying measurement equivalence may contribute to present a complete validity evidence. The purpose of this study is to compare the statistical power ratios of methods used for examining the measurement equivalence based on structural equation modeling and item response theory on the artificial data sets generated by diversifying variables of sample size, number of items, and the ratios of the items having differential item function. In accordance with this purpose, the variables have been varied to include three different levels. In the analysis, multi-group confirmatory factor analysis was used which is among the methods based on the structural equation modeling, and likelihood ratio test and comparison of the item parameters methods were used which are among the methods based on item response theory. Multi-group group confirmatory factor analysis (93,50%) and likelihood ratio test (96,75%) methods have reached the highest statistical power ratio in the condition that the sample size is 1000/1000, the number of items is 40 items and the ratios of the items having differential item function is 10%. The method of comparing the item parameters (94,50%) has reached the highest statistical power ratio in the condition of sample size is 1000/1000, the number of items is 20 and the ratios of the items having differential item function are 10-20%.