An asymptotic expression for the reliability of a linearly equated test is developed using normal theory. The reliability is expressed as the product of two terms, the reliability of the test before equating, and an adjustment term. This adjustment term is a function of the sample sizes used to estimate the linear equating transformation. The results of a simulation study indicate close agreement between the theoretical and simulated reliability values for samples greater than 200. Findings demonstrate that samples as small as 300 can be used in linear equating without an appreciable decrease in reliability.

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and Levine, under the nonequivalent groups with anchor test (NEAT) design. A recursive formula for the ASEE is provided for a series of equatings that makes use of only historical summary statistics. This formula can serve as a new tool to measure the magnitude of equating errors that have accumulated over a series of equatings, and to help monitor and design testing programs.

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are compared through the analysis of data sets famous in the equating literature. Also, the classical percentile-rank, linear, and mean equating models are each proven to be a special case of a Bayesian model under a highly-informative choice of prior distribution.