A Comparison Of Error Rates Of Classical Test Theory And Item Response Theory-Based Test Equating Methods Using Simulation Data

Abstract

In educational measurement and evaluation processes, the ability of different test forms to produce comparable scores is critical for obtaining fair and valid results. In this regard, the present study aims to comparatively examine test equating methods based on the Classical Test Theory (CTT) and the Item Response Theory (IRT), which are widely used in measurement applications, in terms of their error levels. Within this scope, using data generated through simulation, the methods of Linear Equating, Equipercentile Equating, Mean-Mean, Mean-Standard Deviation, Stocking-Lord, and Haebara were applied. Excel and R software were utilized for the analyses. In order to determine the amount of error between each raw score and its corresponding equated score, the Weighted Mean Squared Error (WMSE) criterion was used. These error values enabled a comparative evaluation of the accuracy levels of equating methods according to score ranges. The findings revealed that equating methods based on Item Response Theory produced lower error particularly at the extreme ends of the score distribution, whereas methods based on Classical Test Theory provided more consistent results at the mid-range. The study presents the error behaviors of test equating approaches through simulation-based comparisons and contributes to the theoretical discussions in the field of measurement.