Generalizations and Extensions of the Probability of Superiority Effect Size Estimator

Researchers are strongly encouraged to accompany the results of statistical tests with appropriate estimates of effect size. For 2-group comparisons, a probability-based effect size estimator (A) has many appealing properties (e.g., it is easy to understand, robust to violations of parametric assumptions, insensitive to outliers). We review generalizations of the A statistic to extend its use to applications with discrete data, with weighted data, with k > 2 groups, and with correlated samples. These generalizations are illustrated through reanalyses of data from published studies on sex differences in the acceptance of hypothetical offers of casual sex and in scores on a measure of economic enlightenment, on age differences in reported levels of Authentic Pride, and in differences between the numbers of promises made and kept in romantic relationships. Drawing from research on the construction of confidence intervals for the A statistic, we recommend a bootstrap method that can be used for each generalization of A. We provide a suite of programs that should make it easy to use the A statistic and accompany it with a confidence interval in a wide variety of research contexts.