Effect on Equating Results of Matching Samples on an Anchor Test

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Abstract
This article addresses the sample invariant properties of five anchor test equating methods (Tucker and Levine equally reliable linear equating, chained equipercentile, frequency estimation equipercentile equating, and three-parameter item response theory true-score equating). Equating results across two sampling conditions, representative sampling and new-form matched sampling, 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 new-form 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 the Levine and chained equipercentile methods. Results based on the Tucker observed- score equating method and frequency estimation equipercentile equating were found to be essentially the same across representative and new-form matched sample conditions. Results for the five equating methods tended to converge under the new-form matched sample condition. The last section of this paper offers tentative explanations for the findings.