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I have a non-normal distribution data of two independent samples os patients divides by two groups 'control' and 'treatment'. Would like to verify if there are difference between the two groups 'control' and 'treatment' and measure this difference, so I am using the code:

wilcox.test(data.to.work$disease ~ data.to.work$group)

Ok for my test, my doubt is: I can use Cohen's d to measure de effect size?

I also did a test using the codes:

cohens_d(data.to.work$disease ~ data.to.work$group)
rcompanion::wilcoxonR(data.to.work$disease, g=data.to.work$group, ci=T)

Both give large effect size.

May I use Cohen's d ? Or is the second test the most recommended, or some other?

Tks

Phil
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Elias
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    This question might be better for stats.stackexchange.com, as it pertains mostly to statistical interpretation and there is no concrete programming error. – dcsuka Jul 29 '22 at 16:46
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    This question is also asked here: [stats.stackexchange.com/questions/583890/effect-size-for-wilcox-mann-whitney-in-r-cohens-d](https://stats.stackexchange.com/questions/583890/effect-size-for-wilcox-mann-whitney-in-r-cohens-d) – Sal Mangiafico Aug 15 '22 at 14:28

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It would be unusual to pair Cohen's d with a Wilcoxon-Mann-Whitney test. There's no reason that you couldn't calculate it, but probably, if you are choose the WMW test, you wouldn't be that interested in comparing the difference in means of the samples to the pooled standard deviation.

A typical standardized effect size statistic for the WMW test is based on the probability of an observation in one group being larger than an observation in the other group.

These standardized effect size statistics include Vargha and Delaney’s A, Cliff’s delta, Glass rank biserial coefficient, and Grissom and Kim's Probability of Superiority.

Rather than using the wilcoxonR() function, I would recommend a using a different function in that package that calculates one of the effect size statistics mentioned above.

Sal Mangiafico
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