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An analytic procedure for smoothing in equipercentile equating using cubic smoothing splines is described and illustrated. The effectiveness of the procedure is judged by comparing the results from smoothed equipercentile equating with those from other equating methods using multiple cross-validations for a variety of sample sizes. Data on randomly equivalent groups of approximately 3,000 examinees per form from four forms of each of the four tests of the ACT Assessment Program (AAP) were used in this evaluation. Relative to the other equating procedures studied, smoothed equipercentile equating was found to be most adequate for the AAP, especially for the most dissimilar form pairs.
Michael J. Kolen (1984) studied this question.