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.
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Journal of Educational and Behavioral Statistics
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