Evaluating Six Approaches to Handling Zero-Frequency Scores under Equipercentile Equating

Abstract

ABSTRACT In many large testing programs, equipercentile equating has been widely used under a random groups design to adjust test difficulty between forms. However, one thorny issue occurs with equipercentile equating when a particular score has no observed frequency. The purpose of this study is to suggest and evaluate six potential methods in equipercentile equating when an observed-score distribution involves zero-frequency scores. A simulation study involving two levels of test lengths (30 and 50 items), five levels of sample sizes (100, 500, 1000, 3000, and 5000), and two levels of similarity in score distributions between two forms, was conducted to assess these methods in terms of equating accuracy. Results revealed that presmoothing was the most accurate method in estimating the equipercentile equating relationship when the population distributions for two forms differ with respect to the form of score distributions. When the populations have a similar score distribution, the presmoothing method was also found to be the most accurate method with longer tests (50 items). Furthermore, the performance of these methods does not vary as a function of the number of zero-frequency scores. This study informs practitioners of approaches to handling a zero-frequency issue with equipercentile equating that leads to more accurate equating results.