Confidence Intervals for the Probability of Superiority Effect Size Measure and the Area Under a Receiver Operating Characteristic Curve

Abstract

It is good scientific practice to the report an appropriate estimate of effect size and a confidence interval (CI) to indicate the precision with which a population effect was estimated. For comparisons of 2 independent groups, a probability-based effect size estimator (A) that is equal to the area under a receiver operating characteristic curve and closely related to the popular Wilcoxon-Mann-Whitney nonparametric statistical tests has many appealing properties (e.g., easy to understand, robust to violations of parametric assumptions, insensitive to outliers). We performed a simulation study to compare 9 analytic and 3 empirical (bootstrap) methods for constructing a CI for A that can yield very different CIs for the same data. The experimental design crossed 6 factors to yield a total of 324 cells representing challenging but realistic data conditions. Results were examined using several criteria, with emphasis placed on the extent to which observed CI coverage probabilities approximated nominal levels. Based on the simulation study results, the bias-corrected and accelerated bootstrap method is recommended for constructing a CI for the A statistic; bootstrap methods also provided the least biased and most accurate standard error of A. An empirical illustration examining score differences on a citation-based index of scholarly impact across faculty at low-ranked versus high-ranked research universities underscores the importance of choosing an appropriate CI method.