Equating tests under the graded response model

Abstract

The Stocking and Lord (1983) procedure for computing equating coefficients for tests having dichotomously scored items is extended to the case of graded response items. A system of equations for obtaining the equating coefficients under Samejima’s (1969, 1972) graded response model is derived. These equations are used to compute equating coefficients in two related situations. Under the first, the equating coefficients are obtained by matching, on an examinee by examinee basis, the true scores on two tests. In the second case, the equating coefficients are obtained by matching the test characteristic curves (TCCs) of the two tests. Several examples of computing equating coefficients in these two situations are provided. The TCC matching approach was much less demanding computationally and yielded equating coefficients that differed little from those obtained through the true score distribution matching approach. Index terms: equating coefficients, graded response model, quadratic loss function, response function method, Stocking and Lord equating technique, test equating, test characteristic curves.