One desirable property of a measurement process or instrument is the maximum invariance of the results across subpopulations with similar distribution of the traits. Determining measurement invariance (MI) is a statistical procedure in which different methods are used given different factors, such as the nature of the data (e.g. continuous, or discrete, completeness), sample size, measurement framework (e.g. observed scores, latent variable modeling), and other context-specific factors. To evaluate the statistical results, numerical criteria are often used, derived from theory, simulation, or practice. One statistical method to evaluate MI is multiple-group confirmatory factor analysis (MG-CFA) in which the amount of change in fit indices of nested models, such as comparative fit index (CFI), Tucker-Lewis fit index (TLI), and the root mean squared error of approximation (RMSEA), are used to determine if the lack of invariance is non-trivial. Currently, in the MG-CFA framework for establishing MI, the recommended effect size is a change of less than 0.01 in CFI/TLI measures (Cheung & Rensvold, 2002). However, the recommended cutoff value is a very general index and may not be appropriate under some conditions, such as dichotomous indicators, different estimation methods, different sample sizes, and model complexity. In addition, in determining the cutoff value, consequences to the lack of invariance have been ignored in the current research. To address these gaps, the present research undertakes to evaluate the appropriateness of the current effect size of ΔCFI or ΔTLI < 0.01 in educational measurement settings, where the items are dichotomous, the item response functions follow an item response theory (IRT) model, estimation method is robust weighted least squares, and the focal and reference groups differ from each other on the IRT scale by 0.5 units (equivalent to ±1 raw score). A simulation study was performed with five (crossed) factors: percent of differential functioning items, IRT model, IRT a and b parameters, and the sample size. The results of the simulation study showed that the cutoff value of a ΔCFI/ΔTLI < 0.01 for establishing MI is not appropriate for educational settings under the foregoing conditions.