The Asymptotic Equating Methodology and Other Test Equating Evaluation Procedures

Abstract

A methodology is proposed to evaluate the asymptotic performance of test equating methods and of various test equating indices. A test theoretic viewpoint is taken to develop the asymptotic equating methodology and the conditional equating analyses methodology. An asymptotic equating study may be thought of as a simulation study in which sample sizes are infinite. Previous equating evaluation methods are reviewed and critiqued. The advantages of the asymptotic equating methodology and the conditional equating analyses methodology include (1) the ability to evaluate the asymptotic performance of equating methods directly against several equating criteria at any trait or proficiency level, (2) the ability to evaluate the asymptotic performance of any empirical equating evaluation index or procedure, (3) the ability to investigate the asymptotic effects of specific model violations on equating criteria. As an example, the asymptotic equating methodology was applied to a common type of equating design in standardized testing--the "nonequivalent-groups anchor-test design" in which different groups take different tests with some items in common. Important conclusions about commonly used equating methods were revealed by the asymptotic equating methodology and the conditional analysis methodology that had not been clearly demonstrated before. The magnitudes of the asymptotic bias of some commonly used equating methods were clearly revealed. Problems concerning the use of observed measures as infallible estimates of latent variables are also illustrated and emphasized. An integrated equating research program is proposed that includes asymptotic studies, simulation studies, empirical studies.