First among others? Cohen’s d vs. alternative standardized mean group difference measures

Abstract

Standardized effect size measures typically employed in behavioral and social sciences research in the multi-group case (e.g., η2, f2) evaluate between-group variability in terms of either total or within-group variability, such as variance or standard deviation – that is, measures of dispersion about the mean. In contrast, the definition of Cohen’s d, the effect size measure typically computed in the two-group case, is incongruent due to a conceptual difference between the numerator – which measures between-group variability by the intuitive and straightforward raw difference between the two group means – and the denominator which measures within-group variability in terms of the difference between all observations and the group mean (i.e., the pooled within-groups standard deviation, SW). Two congruent alternatives to d, in which the root square or absolute mean difference between all observation pairs is substituted for SW as the variability measure in the denominator of d, are suggested and their conceptual and statistical advantages and disadvantages are discussed.

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