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McGraw and Wong (1992) described an appealing index of effect size, called CL, which measures the difference between two populations in terms of the probability that a score sampled at random from the first population will be greater than a score sampled at random from the second. McGraw and Wong introduced this "common language effect size statistic" for normal distributions and then proposed an approximate estimation for any continuous distribution. In addition, they generalized CL to the n-group case, the correlated samples case. and the discrete values case.In the current paper a different generalization of CL, called the A measure of stochastic superiority, is proposed, which may be directly applied for any discrete or continuous variable that is at least ordinally scaled. Exact methods for point and interval estimation as well as the significance tests of the A = .5 hypothesis are provided. New generalizations of CL are provided for the multi-group and correlated samples cases.Suppose that an experimenter wishes to assess the difference between two populations with respect to a variable X. If X can be measured on an interval scale, and if the expected value can appropriately characterize the level of the variable in the two populations, then one can measure this difference with the la~ -lu2 difference of the corresponding expected values. If one is interested in a standardized difference, where the variability is also taken into account, one can use the expression (p, -p2)/cr. Here ~r is either the common or the pooled SD

Despite pleas from methodologists, researchers often continue to dichotomize continuous predictor variables. The primary argument against this practice has been that it underestimates the strength of relationships and reduces statistical power. Although this argument is correct for relationships involving a single predictor, a different problem can arise when multiple predictors are involved. Specifically, dichotomizing 2 continuous independent variables can lead to false statistical significance. As a result, the typical justification for using a median split as long as results continue to be statistically significant is invalid, because such results may in fact be spurious. Thus, researchers who dichotomize multiple continuous predictor variables not only may lose power to detect true predictor-criterion relationships in some situations but also may dramatically increase the probability of Type I errors in other situations.

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