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Methods of Linking With Small Samples in a Common-Item Design: An Empirical Comparison

Kim, Sooyeon; Livingston, Samuel A.
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Report Number:
ETS Research Report
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Subject/Key Words:
Circle-Arc Method, Small-Sample Equating, Chained Mean Method, Equipercentile Method, Equating Bias, Equating Error


A series of resampling studies was conducted to compare the accuracy of equating in a common item design using four different methods: chained equipercentile equating of smoothed distributions, chained linear equating, chained mean equating, and the circle-arc method. Four operational test forms, each containing more than 100 items, were used for the equating, with new-form samples of 100, 50, 25, and 10 examinees and reference-form samples three times as large. Accuracy was assessed in terms of the root-mean-squared difference (over 1,000 replications) of the sample equatings from the criterion equating. Overall, chained mean equating produced the most accurate results for low scores, but the circle-arc method produced the most accurate results, particularly in the upper half of the score distribution.

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