An Analytic Comparison of Effect Sizes for Differential Item Functioning

Three types of effects sizes for DIF are described in this exposition: log of the odds-ratio (differences in log-odds), differences in probability-correct, and proportion of variance accounted for. Using these indices involves conceptualizing the degree of DIF in different ways. This integrative review discusses how these measures are impacted in different ways by item difficulty, item discrimination, and item lower asymptote. For example, for a fixed discrimination, the difference in probabilities decreases as the difference between the item difficulty and the mean ability increases. Under the same conditions, the log of the odds-ratio remains constant if the lower asymptote is zero. A non-zero lower asymptote decreases the absolute value of the probability difference symmetrically for easy and hard items, but it decreases the absolute value of the log-odds difference much more for difficult items. Thus, one cannot set a criterion for defining a large effect size in one metric and find a corresponding criterion in another metric that is equivalent across all items or ability distributions. In choosing an effect size, these differences must be understood and considered.