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Behav Res Methods. 2016 Dec;48(4):1560-1574.

Effect size measures in a two-independent-samples case with nonnormal and nonhomogeneous data.

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Department of Psychology, University of Manitoba, P517B, Duff Roblin Building, Winnipeg, Manitoba, R3T 2N2, Canada.


In psychological science, the "new statistics" refer to the new statistical practices that focus on effect size (ES) evaluation instead of conventional null-hypothesis significance testing (Cumming, Psychological Science, 25, 7-29, 2014). In a two-independent-samples scenario, Cohen's (1988) standardized mean difference (d) is the most popular ES, but its accuracy relies on two assumptions: normality and homogeneity of variances. Five other ESs-the unscaled robust d (d r* ; Hogarty & Kromrey, 2001), scaled robust d (d r ; Algina, Keselman, & Penfield, Psychological Methods, 10, 317-328, 2005), point-biserial correlation (r pb ; McGrath & Meyer, Psychological Methods, 11, 386-401, 2006), common-language ES (CL; Cliff, Psychological Bulletin, 114, 494-509, 1993), and nonparametric estimator for CL (A w ; Ruscio, Psychological Methods, 13, 19-30, 2008)-may be robust to violations of these assumptions, but no study has systematically evaluated their performance. Thus, in this simulation study the performance of these six ESs was examined across five factors: data distribution, sample, base rate, variance ratio, and sample size. The results showed that A w and d r were generally robust to these violations, and A w slightly outperformed d r . Implications for the use of A w and d r in real-world research are discussed.


Common-language effect size; Nonnormal data; Simulation; Unequal variances

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