AN ALTERNATIVE TO EQUATING WITH SMALL SAMPLES IN THE NON-EQUIVALENT GROUPS ANCHOR TEST DESIGN

Abstract

This study addresses the sample error and linking bias that occur with small and unrepresentative samples in a non-equivalent groups anchor test (NEAT) design. We propose a linking method called the synthetic function, which is a weighted average of the identity function (the trivial equating function for forms that are known to be completely parallel) and a traditional equating function (in this case, the chained linear equating function) used in the normal case in which forms are not completely parallel. Specifically, we compare the synthetic, identity, and chained linear functions for various-sized samples from two types of national assessments. One design uses a high reliability test and an external anchor, and the other uses a relatively low reliability test and an internal anchor. The chained linear equating functions derived from the total sample are used as the criterion equating function in both assessments. The results from each of these methods were compared to the criterion equating function with respect to linking bias and error. The study indicates that the synthetic functions might be a better choice than the chained linear equating method when samples are neither large nor representative.