Equating error in observed-score equating

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of test takers on one version of the test to make them indistinguishable from those on another, equating error should be defined as the degree to which the equated scores realize this goal. Two equivalent definitions of equating error based on this criterion are formulated. It is shown how these definitions allow one to evaluate such key quantities as the bias and mean squared error of any equating method if the tests fit a unidimensional response model. Several alternative applications of the ideas for the case in which the tests do not fit a unidimensional response model are discussed.