Equating an adaptive test to a linear test

Two new methods for the equating of an adaptive test to a linear test are presented. The methods are based on the conditional distributions of the observed scores on the two tests, given the examinee’s ability. They are motivated by the fact that conditioning on the examinee’s ability is necessary to allow for differences between observed-score distributions of examinees. The two methods were evaluated empirically against the traditional equipercentile method based on the marginal score distributions on the two tests and a method that uses the test characteristic function (TCF) of the linear test. The criterion in this study was the difference between the distribution of the equated score and the actual observed score on the linear test. The two conditional methods were unbiased and had mean-squared error in the equated scores comparable to the marginal equipercentile method and the TCF methods. The last two methods were strongly biased. It is argued that their bias is a consequence of the fact that they use a single equating transformation for an entire population of examinees and, therefore, have to compromise between the individual score distributions.