Investigations of a nonparametric effect size statistic for studies with two independent samples
Cohen’s d is a widely-reported standardized effect size statistic in research. Research has established that Cohen’s d does not perform well in the presence of non-normal and heteroscedastic data. Robust expressions of d are available, but few nonparametric alternative effect size statistics exist. A nonparametric analogue of Cohen’s d effect size, using median and median absolute deviation, is proposed and its characteristics are explored. Using simulated data, the proposed effect size, ΔMAD, is found to be a more accurate measure of group differences for data sets that include outliers. Simulations also show that that ΔMAD is also a more appropriate measure of group differences for non-normal and/or heteroscedastic data. Surprisingly, these simulations indicate that ΔMAD provides a better estimate of effect size than Cohen’s d even when the usual tests (e.g., Levene test for equality of variances, Shapiro-Wilk normality test) fail to detect significant deviations from normality and/or equal variance. An investigation of additional useful properties of ΔMAD as an instrument for meta-analyses, and the implications of this study for meta-analyses, are presented.
Ricca, Bernard P. and Blaine, Bruce E., "Investigations of a nonparametric effect size statistic for studies with two independent samples" (2018). Mathematical and Computing Sciences Faculty/Staff Publications. Paper 23.
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