## Choice of effect size for Mann-Whitney/Wilcoxon tests

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## Choice of effect size for Mann-Whitney/Wilcoxon tests

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!
Bobafett

Posts: 18
Joined: Thu Jul 18, 2019 11:33 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

hi,

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

jonathon

jonathon

Posts: 1763
Joined: Fri Jan 27, 2017 10:04 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

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...

Cheers
Paul

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.
Bobafett

Posts: 18
Joined: Thu Jul 18, 2019 11:33 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

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

Posts: 28
Joined: Sun Jul 02, 2017 1:35 pm

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

Hello,

The best would be to use a non-parametric effect size like Vargha & Delaney Â measure of dominance. It is implemented in the RProbSup R package. With that package, you will also get the confidence interval around the effect size. I advise you read that article: https://www.researchgate.net/profile/Jo ... esigns.pdf

Peng, C.-Y. J., & Chen, L.-T. (2014). Beyond Cohen's d : Alternative Effect Size Measures for Between-Subject Designs. The Journal of Experimental Education, 82(1), 22-50. doi:10.1080/00220973.2012.745471

"[Â] estimate[s] the degree of one distribution dominating over the other distribution" (p.40)

"Of the nine estimators summarized in Table 2b, we recommend the four estimators of dominance in Category (B) to supplement Cohen’s d to conceptualize ES beyond mean differences. Of these four estimators, Vargha and Delaney’s Â stands out for its meaningful interpretability in terms of stochastic equality/superiority or stochastic homogeneity/heterogeneity in a variety of research contexts and for a variety of data types. Compared to Cohen’s d, Vargha and Delaney’s Â represents a radical reconceptualization of ES with sound statistical properties and well developed theoretical framework." (p.45)

That would be great if Jamovi could provide the Â effect size.
Mik

Posts: 1
Joined: Tue Oct 29, 2019 3:29 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

Hello everyone,
I would like to come back to Bobafett's question about the z-value and the effect size r for the Wilcoxon signed rank test.
According to APA-style I have to report the results of the Wilcoxon signed rank test like this: Z(N) = value, p = value, r = value.

Can someone explain to me how I can get the z-value as well as the r-value based on the values that jamovi gives me ?
I have already come across various converters on the net, but they provide different values...

Cheers,
Lisa
Lisa

Posts: 15
Joined: Fri May 29, 2020 7:53 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

hmm, i'm afraid i don't know anything about a Z or an r value in the context of WSR ... i thought WSR produced a W-statistic.

i'll be interested to hear what others say.

kind regards

jonathon

Posts: 1763
Joined: Fri Jan 27, 2017 10:04 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

Hi Jonathan,
thank you for the quick response.
How would you report the results of Wilcoxon signed rank test according to jamovi output then?
Lisa

Posts: 15
Joined: Fri May 29, 2020 7:53 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

i'd report the W-statistic and the p-value.

jonathon

jonathon

Posts: 1763
Joined: Fri Jan 27, 2017 10:04 am

## Re: Choice of effect size for Mann-Whitney/Wilcoxon tests

Unfortunately I have to present my results according to APA guidelines. These require the Z-value in the WSR test.
SPSS usually displays a Z-value with which I can also calculate the r-value but I prefer working with jamovi instead of SPSS...

I used this website to calculate Z-Value: http://www.statskingdom.com/175wilcoxon_signed_ranks.html
Lisa

Posts: 15
Joined: Fri May 29, 2020 7:53 am

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