Comparisons among Small Sample Equating Methods in a Common‐Item Design

Abstract

Score equating based on small samples of examinees is often inaccurate for the examinee populations. We conducted a series of resampling studies to investigate the accuracy of five methods of equating in a common‐item design. The methods were chained equipercentile equating of smoothed distributions, chained linear equating, chained mean equating, the symmetric circle‐arc method, and the simplified circle‐arc method. Four operational test forms, each containing at least 110 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 described 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 two circle‐arc methods produced the most accurate results, particularly in the upper half of the score distribution. The difference in equating accuracy between the two circle‐arc methods was negligible.