Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method

This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample sizes (300, 1,000, and 3,000) and for three test content areas (ITBS Maps and Diagrams, ITBS Reference and Materials, and ITBS Capitalization). Ten thousand random samples were simulated from population distributions, and the standard error, bias, and RMSE statistics were calculated. The cubic B-spline presmoothing method performed well in reducing total error of equating, whereas the direct presmoothing method appeared to need some modification for it to be as accurate as other smoothing methods.