East Carolina University
Department of Psychology

Nonparametric Effect Size Estimators

    I have received several queries from persons asking for advice on how to estimate effect sizes when comparing two groups with a nonparametric procedure such as the Wilcoxon rank sum test.  I am no expert on this, but it appears that there is some good advice out there to be had.  Here is what I have been able to gather.

    First, remember that these procedures do not test the same null hypothesis that a parametric t test or ANOVA tests.  The nonparametric null hypothesis is that the populations be compared are identical in all aspects -- not just in location.  If you are willing to assume that the populations do not differ in dispersion or shape, then you can interpret a significant difference as a difference in locations.  I shall assume that you are making such assumptions.

    It would seem reasonable to me to report the same effect size estimates that you would report with a parametric analysis, but using ranked data.  For example, with two independent samples just rank the data and then compute Hedges g (estimate of Cohen's d).

    I posted a query about this on EDSTAT-L and got a few responses, which I provide here.

    Leech (2002) suggested to report nonparametric effect size indices, such as Vargha & Delaney's A or Cliff's d. (Leech (2002). A Call for Greater Use of Nonparametric Statistics. Paper presented at the Annual Meeting of the Mid-South Educational Research Association, Chattanooga, TN, November 6-8.)

John Mark, Regions University.

    I have not found the time to check out the Grissom and Kim book.

    If you find any good Internet resources on this topic, please do pass them on to me so I can include them here.  Thanks.

Return to Dr. Wuensch's Statistical Resources Page

Contact Information for the Webmaster,
Dr. Karl L. Wuensch

This page most recently revised on 5. January 2008