Kernel Equating Presmoothing Methods: An Empirical Study with Mixed-Format Test Forms

When equating test forms, it is common to presmooth the test score distributions before conducting the equating. In this study, the log-linear and item response theory (IRT) presmoothing methods were compared when equating mixed-format test forms using kernel equating. Test forms from two different high-stakes tests were equated: The Swedish national test in mathematics, using the equivalent group sampling design, and the verbal part of the Swedish SAT test, using the nonequivalent groups with anchor test sampling design. In both cases, the analytical equating standard errors were lower for high and low performing test takers when using IRT presmoothing compared to log-linear presmoothing. Both presmoothing methods resulted in reasonable equated curves. As no true equating transformation is known in a practical setting, using IRT models for presmoothing appears to be a viable alternative to log-linear models when equating mixed-format tests such as the Swedish SAT.