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Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true score equating; and (4) beta 4 observed score equating. Four subtests of the Iowa Tests of Basic Skills, with two forms of each test and a random sample of 3,000 examinees for each form were used. Results show that true score equating more closely achieved FOE than observed score equating, while observed score equating more closely achieved SOE, CMSE difference, and equipercentile equating property than true score equating. Among the four equating methods, 3PL observed most closely achieved SOE and had the smallest CMSE difference, and beta 4 observed was the method that most closely met the equipercentile equating property. (Contains 6 tables, 7 figures, and 26 references.) (SLD)

This study compared various equating models and procedures for a sample of data from the Medical College Admission Test(MCAT), considering how item response theory (IRT) equating results compare with classical equipercentile results and how the results based on use of various IRT models, observed score versus true score, direct versus linked equating, and various test forms compare. The practical issues and potential benefits of IRT equating are discussed. Data were from 2 forms of the test and 2 administrations, for sample sizes of 8,494, 3,638, 8,147, and 4,478. Choosing between equipercentile and IRT equating impacted MCAT scores. For the Biological Sciences, the effect of using any IRT model would appear to be minimal, but none of the IRT model equivalents for Physical Science and Verbal Reasoning exactly matched those of equipercentile equating. Each IRT model diverged from equipercentile equating in Physical Sciences, with the one-parameter model most discrepant and the three-parameter model least discrepant. IRT model equivalents for the Verbal Reasoning section also diverged from the equipercentile results. Currently, random groups and common-item equating are used for the MCAT, and both of these designs were also considered in this study so that moving to IRT equating need not create design complications, although some statistical assumptions associated with IRT models must be met. Some of the issues in using IRT equating, including choosing a calibration program and IRT model, are discussed. (Contains 12 figures, 37 tables, and 20 references.) (SLD)