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Lets assume that I am comparing pre intervention weight and post intervention weight of the participant (paired data). From Wilcoxon Matched-Pairs Signed-Ranks Test I and got p-value 0.03. Am I understand correctly that I should report in results "median of paired difference" like this:

The result of Wilcoxon Matched-Pairs Signed-Ranks Test with paired data shows that the weight of the participant after intervention is lower than the weight before intervention (p-value 0.03) with a median of paired difference decrease by 5 lb and with small effect size (d=0.37).

or I should report "median difference" like:

The result of Wilcoxon Matched-Pairs Signed-Ranks Test with paired data shows that the weight of the participant after intervention is lower than the weight before intervention (p-value 0.03) with a median difference decrease by 5 lb and with small effect size (d=0.37).

or maybe some other way?

vasili111
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    A couple of comments: 1) In general the signed rank test is not a test of medians. 2) The first step in the signed rank test is to subtract the values of the pairs. From there, the test is conducted on this single vector of difference values. I don't know if this helps in thinking about the appropriate language. – Sal Mangiafico Oct 25 '22 at 00:39
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    Perhaps see: stats.stackexchange.com/questions/593445/exactly-what-does-the-wilcoxon-signed-rank-test-compare . – Sal Mangiafico Oct 25 '22 at 00:39
  • Are you using Cohen's d as an effect size statistic ? – Sal Mangiafico Oct 25 '22 at 00:40
  • @SalMangiafico Thank you. Could you please give me the example what is the correct way to interpret result? I am using Cohens d for effect size. – vasili111 Oct 25 '22 at 15:28
  • I don't know that I have a good example to look at. But a couple of comments: 1) As far as I can see, the only difference in your two paragraphs is the removal of "of paired". I'm not sure that those words make a difference in meaning here. Maybe. It depend on what you actually intend. 2) The signed rank test is not generally a test of medians, but it's fine to report the median of the differences. 3) It's weird to use Cohen's d as an effect size measurement with the signed rank test, as this statistic is based on means and standard deviations, which aren't used by the signed rank test. – Sal Mangiafico Oct 25 '22 at 15:47
  • @SalMangiafico Thank you. Which effect size do you recommend to use here? – vasili111 Oct 25 '22 at 15:53

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