Kernel Equating Using Propensity Scores for Nonequivalent Groups

When equating two test forms, the equated scores will be biased if the test groups differ in ability. To adjust for the ability imbalance between nonequivalent groups, a set of common items is often used. When no common items are available, it has been suggested to use covariates correlated with the test scores instead. In this article, we reduce the covariates to a propensity score and equate the test forms with respect to this score. The propensity score is incorporated within the kernel equating framework using poststratification and chained equating. The methods are evaluated using real college admissions test data and through a simulation study. The results show that propensity scores give an increased equating precision in comparison with the equivalent groups design and a smaller mean squared error than by using the covariates directly. Practical implications are also discussed.