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A Comparison of Observed Score and True Score Equating Methods for Representative Samples and Samples Matched on an Anchor Test IRT

Lawrence, Ida M.; Dorans, Neil J.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Equated Scores, Item Response Theory (IRT), Research Design, Sampling, Statistical Analysis


This paper addresses the sample invariant properties of four equating methods (Tucker and Levine linear equating, Equipercentile equating through an anchor test, and three-parameter item response theory equating). Equating results across two sampling conditions, "representative" sample and "matched" sample, were compared to determine which equating procedures produced the most consistent results. In the representative sample condition, equatings were based on old-form and new-form samples that differed in ability; in the matched sample condition, the old-form sample was selected to match the anchor test score distribution of the new-form sample. Results for the item response theory equating method differed for representative and matched samples, as did the equating results for Levine and Equipercentile methods. Results based on the Tucker observed-score equating method were found to be essentially the same across representative and matched sample conditions. Results for the four equating methods tended to converge under the matched sample condition. The last section of this paper offers tentative explanations for the findings. (26pp.)

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