Adequacy of Asymptotic Normal Theory in Estimating Reliability for Mastery Tests Based on the Beta-Binomial Model

Abstract

Simulated data based on five test score distributions indicate that a slight modification of the asymptotic normal theory for the estimation of the p and kappa indices in mastery testing will provide results which are in close agreement with those based on small samples from the beta-binomial distribution. The modification is achieved through the multiplication of the asymptotic standard errors of estimate by the constant 1 + 1/m^¾ where m is the sample size.