Practical Application of a Synthetic Linking Function on Small-Sample Equating

Abstract

The synthetic function is a weighted average of the identity (the linking function for forms that are known to be completely parallel) and a traditional equating method. The purpose of the present study was to investigate the benefits of the synthetic function on small-sample equating using various real data sets gathered from different administrations of tests from a licensure testing program. We investigated the chained linear, Tucker, Levine, and mean equating methods, along with the identity and the synthetic functions with small samples (N = 19 to 70). The synthetic function did not perform as well as did other linear equating methods because test forms differed markedly in difficulty; thus, the use of the identity function produced substantial bias. The effectiveness of the synthetic function depended on the forms' similarity in difficulty.

Notes

¹Not all states use the same cut scores for the test.

²The total number of examinees was smaller than the total number of examinees from each of the individual administrations, because only the first record was included for test repeaters.

³Due to ambiguity in item content, one item was not scored in each test form, X and Y. As a result, the possible raw score range of the test forms (X and Y) was the same (119, not 120).

⁴The total number of examinees was smaller than the total number of examinees from each of the individual administrations because only the first record is included for test repeaters.