Empirical Sampling Distributions of Equating Coefficients for Graded and Nominal Response Instruments

Abstract

The sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring were examined. Simulated data were generated under these two models in both horizontal and vertical equating situations for three different types of target tests. The obtained sampling distributions of the equating coefficients were approximately bell-shaped, had small variances, and no outliers or other abnormalities. However, the distributions of the minimum values of the quadratic loss function for the graded response model had outliers that were due to misordered boundary curve location parameter estimates. The means of the sampling distributions of the equating coefficients corresponded to values appropriate for the specific situations used.