Effect size measures in a two-independent-samples case with nonnormal and nonhomogeneous data - Behavior Research Methods
In psychological science, the โnew statisticsโ refer to the new statistical practices that focus on effect size (ES) evaluation instead of conventional null-hypothesis significance testing (Cumming, Psychological Science, 25, 7โ29, 2014). In a two-independent-samples scenario, Cohenโs (1988) standardized mean difference (d) is the most popular ES, but its accuracy relies on two assumptions: normality and homogeneity of variances. Five other ESsโthe unscaled robust d (d r * ; Hogarty & Kromrey, 2001), scaled robust d (d r ; Algina, Keselman, & Penfield, Psychological Methods, 10, 317โ328, 2005), point-biserial correlation (r pb ; McGrath & Meyer, Psychological Methods, 11, 386โ401, 2006), common-language ES (CL; Cliff, Psychological Bulletin, 114, 494โ509, 1993), and nonparametric estimator for CL (A w ; Ruscio, Psychological Methods, 13, 19โ30, 2008)โmay 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.