Ability Metric Transformations Involved in Vertical Equating Under Item Response Theory

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Abstract
The metric transformations of the ability scales in volved in three equating techniques—external anchor test, internal anchor test, and a pooled groups proce dure—were investigated. Simulated item response data for two unique tests and a common test were obtained for two groups that differed with respect to mean abil ity and variability. The obtained metrics for various combinations of groups and tests were transformed to a common metric and then to the underlying ability metric. The results showed that there was reasonable agreement between the transformed obtained metrics and the underlying ability metric. They also showed that the largest errors in the ability score statistics oc curred under the external anchor test procedure and the smallest under the pooled procedures. Although the pooled procedure performed well, it was affected by unequal variances in the two groups of examinees.

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