A quadratic curve equating method to equate the first three moments in equipercentile equating

Abstract

A quadratic curve test equating method for equating different test forms under a random-groups data collection design is proposed. This new method extends the linear equating method by adding a quadratic term to the linear function and equating the first three central moments (mean, standard deviation, and skewness) of the test forms. Procedures for implementing the method and related issues are described and discussed. The quadratic curve method was evaluated using real test data and simulated data in terms of model fit and equating error, and was compared to linear equating, and unsmoothed and smoothed equipercentile equating. It was found that the quadratic curve method fit most of the real test data examined and that when the model fit the population, this method could perform at least as well as, or often even better than, the other equating methods studied. Index terms: equating, equipercentile equating, linear equating, model-based equating, quadratic curve equating, random-groups equating design, smoothing procedures.