DFIT provides a set of functions to calculate the noncompensatory (NCDIF), compensatory (CDIF) and test level (DTF) differential functioning indices for items and tests under Raju's (Raju, Van der Linden & Fleer, 1995) DFIT framework. It also provides functions for obtaining cut-off points for identifying differential functioning for these indices following the Monte Carlo Item Parameter Replication approach proposed by Oshima, Raju & Nanda (2006). This package also improves upon available DFIT software by allowing the covariance matrices for both focal and reference groups to be used. This improves the obtained cut-off points, which result in type I error rates at the nominal level, and increased power, when compared to the cut-off points obtained when using only the focal group item parameter estimates and their estimate covariances (Cervantes, 2012, 2017). Furthermore, this package includes functions for obtaining the asymptotic covariance matrices of item parameter estimates (currently only for dichotomous IRT models) and for calculating the DFIT indices base on the focal group distribution as well as ability estimates for a sample from the focal population are included; these enable ad hoc and a priori power calculations for given item parameters and sample sizes to be possible with this package. Some additional DIF Statistics for which the IPR approach may be applied are also implemented in the package. They include Raju's Area Measures (Raju, 1988) and a generalized Mantel-Haenszel statistic (Roussos, Schnipke & Pashley, 1999). References Cervantes, V.H. (2012). On using the Item Parameter Replication (IPR) Approach for Power Calculation of the Noncompensatory Differential Item Functionin (NCDIF) Index. In: C Arce, G Seoane (eds.), V European Congress of Methodology - Book of Abstracts, pp. 206-207. Universidade de Santiago de Compostela, Santiago de Compostela. Cervantes, V.H. (2017). DFIT: An R Package for Raju's Differential Functioning of Items and Tests Framework. Journal of Statistical Software, 76(5), 1-24. doi:10.18637/jss.v076.i05 Oshima, T.C., Raju, N.S., Nanda, A.O. (2006). A New MEthod for Assessing the Statistical Significance in the Differential Functioning of Items and Tests (DFIT) Framework. Journal of Educational Measurement, 43(1), 1-17. doi:10.1111/j.1745-3984.2006.00001.x Raju, N.S. (1988). The Area Between Two Item Characteristic Curves. Psychometrika, 53(4), 495-502. doi:10.1007/bf02294403 Raju, N.S., van der Linden, W., Fleer, P.F. (1995). IRT-Based Internal Measures of Differential Functioning of Items and Tests. Applied Psychological Measurement, 19(4), 353-368. doi:10.1177/014662169501900405 Roussos, L., Schnipke, D., Pashley, P. (1999). A Generalized Formula for the Mantel-Haenszel Differential Item Functioning Parameter.Journal of Educational and Behavioral Statistics, 24(3), 292-322. doi:10.3102/10769986024003293