Influence of equal or unequal comparison group sample sizes on the detection of differential item functioning using the Mantel–Haenszel and logistic regression techniques

Abstract

In recent decades several methods have been developed for detecting differential item functioning (DIF), and many studies have aimed to identify both the conditions under which items may or may not be adequate and the factors which affect their power and Type I error. This paper describes a Monte Carlo experiment that was carried out in order to analyse the effect of reference group sample size, focal group sample size and the interaction of the two on the power and Type I error of the Mantel–Haenszel (MH) and Logistic regression (LR) procedures. The data were generated using a three-parameter logistic model, the design was fully-crossed factorial with 12 experimental conditions arising from the crossing of the two main factors, and the dependent variables were power and the rate of false positives calculated across 100 replications. The results enabled the significant factors to be identified and the two statistics to be compared. Practical recommendations are made regarding use of the procedures by psychologists interested in the development and analysis of psychological tests.