Standard Errors of Equating for the Percentile Rank–Based Equipercentile Equating With Log-Linear Presmoothing

Abstract

Holland and colleagues derived a formula for analytical standard error of equating using the δ-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank–based equipercentile equating with log-linear smoothing. This procedure is illustrated with real test data and is evaluated using both the bootstrap and the parametric bootstrap (simulation) methods for three different equating designs.