Choice of effect size for Mann-Whitney/Wilcoxon tests

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by Bobafett » Thu Jul 18, 2019 12:58 pm

Hi all,
First of all let me say what a great job you're doing with jamovi - it's a fantastic tool to teach statistics with. I trialled it with our postgraduate students this year, and we're rolling it out to our undergraduate students this coming academic year.

I have a query about the choice of effect size for running Mann-Whitney or Wilcoxon Signed Ranks analyses - both default to reporting Cohen's d (presumably as they are sub-options in the t-test analyses). However, I was always taught to use r - as in 'Z / sqrt #data points' in the instance of these non-parametric equivalents and this is what we've previously taught students to use when running SPSS.

Is it possible to have this calculated instead of or as well as Cohen's d when selecting the non-parametric option?

Cheers - and keep up the good work!
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by jonathon » Fri Jul 19, 2019 2:03 am


i feel like using a square root with non-parametric data is problematic. so with parametric data, there's some mathematical foundation for using squares, and summing them, but i think that's all possible because we know that two is twice one, etc.

but with non-parametric data, we don't know that two isn't ten times one, or a hundred times one, so i don't feel like taking square roots would be a correct approach ... (but you're possibly getting the impression that i only grasp this stuff intuitively). i probably need ravi to chime in.

could you point us to an article which explains it?

with thanks

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by Bobafett » Fri Aug 30, 2019 11:18 am

Hi Jonathon,
Apologies for the delay in posting a reply - summer came and went!

My issue with using Cohen's d is that these are derived from differences in means and SD which are not really applicable to non-parametric statistics - and goes against why we would advocate using NPs to our students . For the past few years I've used the above r calculation when reporting effect sizes and used Andy Field's text book 'Discovering Statistics using SPSS' (3rd Ed). I've since read up on this issue a little more and found a discussion thread on Researchgate which indicates this calculation was proposed by Rosenthal*. The thread also proposes other formula which subsequent contributors have queried, so I guess there does not appear to be a clear consensus on this issue...


Rosenthal (1994). Parametric measures of effect size. In H. Cooper & L. V. Hedges (Eds.), The handbook of research synthesis. (pp. 231-244). New York: Russell Sage Foundation.
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by coledavis » Tue Sep 10, 2019 9:29 pm

For what it's worth, I believe that Hedges' g is preferred to Cohen's d where there are less than 20 cases.
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