Confidence Intervals for True Scores Using the Skew-Normal Distribution

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.