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An Empirical Comparison of Methods for Equating With Randomly Equivalent Groups of 50 to 400 Test Takers

Livingston, Samuel A.; Kim, Sooyeon
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Equating, Random Groups, Small Samples, Circle-Arc Method, Resampling (Statistics)


A series of resampling studies investigated the accuracy of equating by four different methods in a random groups equating design with samples of 400, 200, 100, and 50 test takers taking each form. Six pairs of forms were constructed. Each pair was constructed by assigning items from an existing test taken by 9,000 or more test takers. The criterion equating was the direct equipercentile equating in the full group. Accuracy was described in terms of the root-mean-squared deviation (over 1,000 replications) of the sample equatings from the criterion equating. The equating methods investigated were equipercentile equating of smoothed distributions, linear equating, mean equating, and circle-arc equating; they were compared with each other and with the identity. Circle-arc equating produced the most accurate results for all sample sizes investigated, particularly in the upper half of the score distribution.

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