A Strategy for Replacing Sum Scoring

Abstract

This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and about 12% for a classroom test. A new parametric density function for ability estimates, the tilted scaled β, is used to resolve the nonidentifiability of the univariate test theory model. Item characteristic curves (ICCs) are represented as basis function expansions of their log-odds transforms. A parameter cascading method along with roughness penalties is used to estimate the corresponding log odds of the ICCs and is demonstrated to be sufficiently computationally efficient that it can support the analysis of large data sets.