Small‐Sample Equating Using a Synthetic Linking Function

Abstract

This study addressed the sampling error and linking bias that occur with small samples in a nonequivalent groups anchor test design. We proposed a linking method called the synthetic function, which is a weighted average of the identity function and a traditional equating function (in this case, the chained linear equating function). Specifically, we compared the synthetic, identity, and chained linear functions for various‐sized samples from two types of national assessments. One design used a highly reliable test and an external anchor, and the other used a relatively low‐reliability test and an internal anchor. The results from each of these methods were compared to the criterion equating function derived from the total samples with respect to linking bias and error. The study indicated that the synthetic functions might be a better choice than the chained linear equating method when samples are not large and, as a result, unrepresentative.