A comparison of kernel equating and traditional equipercentile equating methods and the parametric bootstrap methods for estimating standard errors in equipercentile equating.

摘要

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response theory (2-PL IRT) model was used to create population score distributions for different test sizes. Samples were drawn from the populations for different examinee sizes and the equating methods were evaluated using a criterion equating, which was an equipercentile equating function using the entire populations. Bias, standard errors, and root mean squared difference (RMSD) were used as measures to compare the methods to the criterion equating. The results show that KE and its traditional analogues are comparable under the EG design. However, under the NEAT design for which populations were created substantially different in this study, only the Post-stratification equating (PSE) with small or optimal bandwidth can produce results similar to those from the traditional frequency estimation method. Using the same data for equating under the EG design, the parametric bootstrap method was compared to the nonparametric bootstrap method and the analytic method. The results indicated that the parametric method resulted in more accurate estimates of standard errors of equating for all test and sample sizes considered than the other methods did.