Differential item functioning (DIF) occurs when the probability of responding in a particular category to an item differs for members of different groups who are matched on the construct being measured. The identification of DIF is important for valid measurement. This research evaluates an improved version of Lord's X[superscript 2] Wald test for comparing item response model parameter estimates between two groups. The improved version uses better approaches for computation of the covariance matrix and equating the item parameters across groups. There are two equating algorithms implemented in IRTPro and flexMIRT software: Wald-1 (one-stage) and Wald-2 (two-stage), only one of which has been studied in simulations before. The present study evaluates for the first time the Wald-1 algorithm and Wald-1 and Wald-2 for three groups simultaneously. A comparison to two-group IRT-LR-DIF is included. Results indicate that Wald-1 performs very well and is recommended, whereas Type I error is extremely inflated for Wald-2. Performance of IRT-LR-DIF and Wald-1 was similar, even for three groups. (Contains 3 tables.)