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pretty basic question here. I'm pretty sure similar questions have been asked before (if you have any references that may help, you can send them too). Thanks in advance!

I conducted some Wilcoxon tests and would like to report the results in a table. Is it wrong to report the data as means +/- standard deviations, since I used non-parametric tests? I've been told it's standard to report the data as medians + ranges.

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  • $\begingroup$ Do you mean the mean $\pm$ standard errors? $\endgroup$ – Dave Jul 25 at 18:48
  • $\begingroup$ Hahaha sorry Dave. Yes, I mean standard errors. I've been told I can report mean +/- standard deviation, but after a quick Google search, I've come to understand the difference. I've been searching how to report "non-parametric data", and the jury still seems out on this one. Some argue that there is no such thing as non-parametric data, and you can present means or medians as you see fit. I wanted confirmation that this was or was not the case, as I've also been told that I shouldn't present my "non-parametric data" using means. Thanks! $\endgroup$ – bagel Jul 25 at 21:13
  • $\begingroup$ What do others in your field do when they use the Wilcoxon test? What do you hope to do by giving some kind of interval around the mean (or median)? $\endgroup$ – Dave Jul 25 at 21:16
  • $\begingroup$ Hmmm... in all the studies published in this particular field, only one used Wilcoxon tests (with a much smaller sample size) and reported medians instead of means. I initially hoped to give readers a measure of how far my sample's mean was from the the population mean. $\endgroup$ – bagel Jul 25 at 22:08
  • $\begingroup$ It's rather mean +- standard deviation, not standard error if the alternative is median/range. That does not provide an answer to the question though. $\endgroup$ – Michael M Jul 26 at 16:55
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There is nothing wrong with means +/- standard deviations as alternative to median/range. It is primarily a matter of the overall presentation.

I think for presenting Wilcoxon Signed-rank test results somewhat like: "The WSRT suggested that the median sample B ranks (10.4) were statistically significant lower than the median sample A ranks (31.0); $N$= 1015, $p<0.01$." is adequate. This briefly outlines our null hypothesis is that $a - b$ comes from a distribution with zero median (or a bit more formally that their paired rank differences are symmetrically distributed around zero) and can be immediately put in a table format. We can report the test statistic $W$ or the standard error associated with it but it is a bit redundant as most of the information associated with it can be seen in the $p$-value. Given that our data might be somewhat skewed, we might report the interquartile range (IQR) as a non-parametric alternative to the spread of values but again that mostly a matter of personal preference.

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