Confidence Intervals for True Scores Using the Skew-Normal Distribution

Abstract

A recent comparative analysis of alternative interval estimation approaches and procedures has shown that confidence intervals (CIs) for true raw scores determined with the Score method—which uses the normal approximation to the binomial distribution—have actual coverage probabilities that are closest to their nominal level. It has also recently been shown that the skew-normal distribution yields a better approximation to the binomial distribution than the normal distribution. This article thus evaluates the benefits of using the skew-normal approximation for interval estimation of true scores. Three different CIs for true scores based on the skew-normal approximation are considered, and a simulation study is conducted whose results reveal that none of these skew-normal CIs is more accurate than the conventional Score CI in terms of probability coverage. Thus, skew-normal CIs, which incur a substantial computational cost, do not seem to be an advisable alternative for interval estimation of true scores.