Enhancing the Equating of Item Difficulty Metrics: Estimation of Reference Distribution

Abstract

Two methods are currently in use at Educational Testing Service (ETS) for equating observed item difficulty statistics. The first method involves the linear equating of item statistics in an observed sample to reference statistics on the same items. The second method, or the item response curve (IRC) method, involves the summation of conditional observed item statistics across the reference population total score frequencies. This article introduces a quick and effective method for obtaining the reference distribution for the transition from the linear equating method to the IRC method without recalculating all the item difficulties. More specifically, a mathematical formula is derived to estimate the score distribution of a reference group that maintains the current item difficulty scale. Future research is needed to compare the performance of the two approaches.