Constant CSEM Achieved Through Scale Transformation and Adaptive Testing

Abstract

Conditional standard error of measurement (CSEM) indicates the level of measurement precision at a particular true score or ability level. Having a constant CSEM across all scores not only simplifies score interpretation and score reporting, but also contributes to the fairness of testing. This paper compares two fundamentally different approaches to achieving constant CSEMs: CSEM stabilizing scale transformations and computer adaptive tests (CATs) with fixed-precision stopping rules. Through conceptual comparison and empirical illustration, this study shows that the two approaches produce score scales that are nonlinearly related to each other, and each achieving the goal of equalizing the CSEMs on its own scale. Procedures for equalizing the CSEMs of a CAT that is not designed to have fixed precision are provided, and implications for transitioning from linear tests with equal CSEMs to CATs are also discussed.