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.