where m is the difference in number of parameters between the augmented and the compact model. The second IRT-based DIF method is called Lord’s chi-square test (Lord, 1980) and is based upon the null hypothesis of equal item parameters in both subgroups and a statistic with a chi-square distribution under the null hypothesis (Magis,2010). Although three different item response models (1PL, 2PL, 3PL) can be fitted, before the analysis item parameters must be scaled with a common metric prior to statistical testing.. The Qj statistic is defined as;