A Critique and Improvement of the CL Common Language Effect Size Statistics of McGraw and Wong

András Vargha and Harold D. Delaney

Journal of Educational and Behavioral Statistics, 2000, vol. 25, issue 2, 101-132

Abstract: 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.

Keywords: group comparison; effect size measures; measure of stochastic superiority; stochastic equality; stochastic homogeneity; Mann-Whitney-Wilcoxon test; Kruskal-Wallis test; Sign-test; Friedman test (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:25:y:2000:i:2:p:101-132

DOI: 10.3102/10769986025002101

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