A Comparison of Four Test Equating Methods

This research evaluated the effectiveness of identifying students’ real gains through the application of four commonly used equating methods: concurrent calibration (CC) equating, fixed common item parameter (FCIP) equating, Stocking and Lord test characteristic curve (TCC) equating, and mean/sigma (M/S) equating. The performance of the four procedures was evaluated using simulated data for a test design with multiple item formats. Five gain conditions (-0.3, -0.1, 0.0, 0.1 and 0.3 on the θ-scale) were built into the simulation to mimic the Ontario Secondary School Literacy Test (OSSLT), the Test provincial de compétences linguistiques (TPCL), the Assessments of Reading, Writing and Mathematics, Primary and Junior Divisions and the applied version of the English Grade 9 Assessment of Mathematics. Twenty replications were conducted. The estimated percentages at multiple achievement levels and in the successful and unsuccessful categories were compared with the respective true percentages obtained from the known θ-distributions. The results across seven assessments showed that the FCIP, TCC and M/S equating procedures based on separate calibrations performed equally well and much better than the CC procedure.