# Are there standards for reporting non-parametric test results?

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.

• Do you mean the mean $\pm$ standard errors? – Dave Jul 25 at 18:48
• 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! – bagel Jul 25 at 21:13
• 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)? – Dave Jul 25 at 21:16
• 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. – bagel Jul 25 at 22:08
• 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. – Michael M Jul 26 at 16:55

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.