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Evaluation of Two New Smoothing Methods in Equating: The Cubic B‐Spline Presmoothing Method and the Direct Presmoothing Method
Author(s) -
Cui Zhongmin,
Kolen Michael J.
Publication year - 2009
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/j.1745-3984.2009.00074.x
Subject(s) - equating , statistics , mathematics , smoothing , smoothing spline , mean squared error , spline interpolation , rasch model , bilinear interpolation
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.