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

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  • András Vargha
  • Harold D. Delaney

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.

Suggested Citation

  • András Vargha & Harold D. Delaney, 2000. "A Critique and Improvement of the CL Common Language Effect Size Statistics of McGraw and Wong," Journal of Educational and Behavioral Statistics, , vol. 25(2), pages 101-132, June.
    • Handle: RePEc:sae:jedbes:v:25:y:2000:i:2:p:101-132
    DOI: 10.3102/10769986025002101
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    Cited by:

    1. Matthew B. Welsh & Steve H. Begg, 2018. "More-or-less elicitation (MOLE): reducing bias in range estimation and forecasting," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 171-212, June.
    2. Chen, Lixin, 2017. "Do patent citations indicate knowledge linkage? The evidence from text similarities between patents and their citations," Journal of Informetrics, Elsevier, vol. 11(1), pages 63-79.
    3. David R. Mandel & Christopher W. Karvetski & Mandeep K. Dhami, 2018. "Boosting intelligence analysts’ judgment accuracy: What works, what fails?," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(6), pages 607-621, November.
    4. repec:cup:judgdm:v:13:y:2018:i:6:p:607-621 is not listed on IDEAS
    5. Alexander Schacht & Kris Bogaerts & Erich Bluhmki & Emmanuel Lesaffre, 2008. "A New Nonparametric Approach for Baseline Covariate Adjustment for Two-Group Comparative Studies," Biometrics, The International Biometric Society, vol. 64(4), pages 1110-1116, December.

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