Choice of effect size for Mann-Whitney/Wilcoxon tests

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by Lisa » Thu Aug 06, 2020 12:48 pm

Hey Jonathon,

thank you for your message which I unfortunaltely have not noticed and read until an hour ago.

Cool, you added an effect size for the Wilcoxon Test!

One last question (I hope so)....How do I have to interpret the biserial rank correlation effect size? Is it the same categorization as for the Pearson correlation coeffient (r = 0,1 small effect/r = 0,3 medium effect/r = 0,5 large effect)?

I´d appreciate your response.

Cheers,
Lisa
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by Lisa » Thu Aug 06, 2020 2:16 pm

...respectively I am wondering why jamovi is using biserial rank correlation instead of Pearson´s product-moment-correlation.

Do you have any Information about that?
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by jonathon » Fri Aug 07, 2020 12:04 am

hi lisa,

i'm not actually the person who implemented it, so i'm not totally sure, but my understanding is that biserial rank in the appropriate effect-size measure for mwu and wsr:

https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test#Effect_size

as for the interpretation, i would *expect* the interpretation of the different magnitudes to be the same. i feel like that's a principle of effect-sizes, but again, i'm more of a software guy than a stats guy.

kind regards

jonathon
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by Lisa » Fri Aug 07, 2020 6:44 am

Hey, Jonathon,
thank you for your feedback and explanations. All right, I understand...
Then who can I contact to answer my questions?
I don´t want to report something without fully understanding it myself.
I've already read through the link you sent. Here, however, it's not clear how the effect size is interpreted. But in my opinion this information is essential for the result report.

Cheers,
Lisa
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by Lisa » Fri Aug 07, 2020 7:12 am

Furthermore I read that biserial rank correlation is used in the presence of a dichotomous variable, which in my case (per-post test with Interval scaled) is not given..
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by Bobafett » Fri Aug 07, 2020 8:40 am

Hi Lisa,
I read a paper by Kerby* which gave a simple formula to calculate the biserial rank correlation - and having used it in Excel I can confirm it gave me the same value as that produced by jamovi. You are correct in that it uses a dichotomous variable - basically the statistic is the direct proportion of 'favourable' vs. 'unfavourable' ranks i.e. the ranks that are supportive of the predicted direction of results vs. those that are not.

Best wishes,
Paul

*Kerby, D. S. (2014) The simple difference formula: an approach to teaching nonparametric correlation. Innovative Teaching, 3, 1.
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by Lisa » Fri Aug 07, 2020 8:48 am

Hi Paul,

thanks a lot for your response.

I read the article too. However, it is still unclear to me how to interpret the strength of the effect (how strong is the effect for example at a value of 0.3 or o.9).
Can you refer to a source in this regard?

In addition, it is still unclear to me why the person-product-moment correlation coefficient is not calculated for two interval-scale variables instead of the biserial rank correlation. Is there an explanation for this?
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by Bobafett » Fri Aug 07, 2020 1:56 pm

Hi Lisa,
Interpreting the size the effect is not entirely clear. I have ran multiple analyses to compare effect sizes generated by biserial correlation, Cohen's d or the r correlation we are both familiar with - but they do not seem to quite tally if interpreting the biserial with the usual .1 .3 and .5 values suggested by Cohen for correlations. However, I did find a worksheet online* which suggests a different rule of thumb for interpreting biserial rank correlations, which seemed to tie things together.

As for why not running a pearson's correlation. Do you mean on the two sets of scores? If so, then that would be addressing something else - the similarity in scores rather than the magnitude of the difference. Apologies if I misunderstood your query.

Paul

*http://core.ecu.edu/psyc/wuenschk/docs30/Nonparametric-EffectSize.pdf
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by Lisa » Sat Aug 08, 2020 6:50 am

Hi, Paul,

thank you for your renewed feedback.

I wonder why jamovi outputs the biserial rank correlation coefficient as effect size for the Wilcoxon Signed Rank Test.
First, because there is hardly any information (as you wrote yourself) on how to interpret it. And to have an effect size of which one does not know how to interpret it makes little sense.
Second, I wonder why jamovi doesn't just output the common effect size r for the Wilcoxon Signed Rank Test.
In the literature (Even in the one you referred to in your last message) you can find everywhere that the biserial rank correlation is performed when a dichotomous variable is present. But if you just want to calculate an are-post comparison using the Wilcocox Signed Rank Test, i.e. if you have a sample that you test at two measuring points and interval-scaled data are available, I don't know why you should calculate/state the biserial rank correlation coefficient here.

Would it not be preferable to output r? I mean for the t-test for dependent samples jamovi also outputs Cohen's d as effect size, so wouldn´t it make sense to do the same for the non-parametric counterpart and output r for the Wilcoxon Signed Rank Test?

I look forward to hearing from you.

Best Wishes,
Lisa
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