Selecting an Equating Method: Linear or Equipercentile?

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Abstract
A new procedure for comparing results of linear and equipercentile equating methods is presented and illustrated. The proposed procedure requires (a) approximating the empirical score distributions of the two forms by means of the first terms of an infinite series, and (b) contrasting the results obtained when only the first two moments are used (i.e., linear equating) with more complete representations. The procedure is demonstrated by calculating the Kolmogorov-Smirnov and Cramer-Von Mises measures of discrepancy for a large number of unimodal distributions approximated by the Edgeworth and Gram-Charlier expansions. The results indicate that both statistics can be accurately predicted on the basis of the skewness and kurtosis of the two distributions. The most attractive feature of the proposed method is that it allows one to calculate the expected degree of efficiency in equating that can be achieved by linear equating, based on the moments of the two relevant distributions.