Comparison of parametric and nonparametric bootstrap methods for estimating random error in equipercentile equating

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams and the ACT English), for two test lengths (24 items and 75 items), and for different parametric models (polynomial log-linear models with fitted degrees of C = 2 through 10). One thousand bootstrap samples were used to estimate standard errors of equating. The parametric bootstrap method was found to estimate standard errors of equating more accurately than the nonparametric bootstrap method in most of the situations examined.