랜덤집단 설계에서 IRT 동등화와 동백분위 동등화의 표준오차의 비교

초록

The random groups design is often used for collecting sample data for test equating. Recently, the item response theory (IRT) based equating methods have been more widely used than the traditional equipercentile equating method. One of the two purposes of this study is to present general formulas for the asymptotic standard errors of equated scores estimated by the IRT true score and observed score equating methods under the random groups design so that they can be used for equating with mixed-format tests. The other purpose is to use empirical test data to examine how the standard errors of equating produced by the IRT equating methods differ from those by the equipercentile equating method. Concerning the second purpose, a comparative study, including various equating conditions, was conducted and the following were found. First, on the average, the IRT observed score equating method resulted in slightly smaller standard errors of equating than the IRT true score equating method, and the two IRT equating methods produced smaller standard errors than the equipercentile equating method which was based on unsmoothed score distributions. Second, the standard errors produced by the three equating methods increased as the lengths of the test forms equated increased and thus the relative frequencies for test scores were lowered. Third, the mean standard errors of equating for the three equating methods decreased as the sample size increased and the amounts of the errors were inversely proportional to the square root of the sample size.

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