ABSTRACT
Consider estimating an effect size that would reflect what would happen if one were able to take each score from Population a and compare it to each score from Population b, one at a time, to see which of the two scores is larger, repeating such comparisons until every score from Population a had been compared to every score from Population b. If most of the time in these pairings of a score from Population a and a score from Population b the score from Population a is the higher of the two, this would indicate a tendency for superior performance in Population a, and vice versa if most of the time the higher score in the pair is the one from Population b. The result of such a method for comparing two populations is a measure of effect size that does not involve comparing the centers of the two distributions, such as means or medians. This effect size is defined as the probability that a randomly sampled member of Population a will have a score (Ya) that is higher than the score (Yb) attained by a randomly sampled member of Population b. This definition will become much clearer in the examples that follow.
