A Comparison of Modern and Popular Approaches to Calculating Reliability for Dichotomously Scored Items

Abstract

Recent work on reliability coefficients has largely focused on continuous items, including critiques of Cronbach’s alpha. Although two new model-based reliability coefficients have been proposed for dichotomous items (Dimitrov, 2003a,b; Green & Yang, 2009a), these approaches have yet to be compared to each other or other popular estimates of reliability such as omega, alpha, and the greatest lower bound. We seek computational improvements to one of these model-based reliability coefficients and, in addition, conduct initial Monte Carlo simulations to compare coefficients using dichotomous data. Our results suggest that such improvements to the model-based approach are warranted, while model-based approaches were generally superior.