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The Pseudo-Median
12th October 2022 By MARS Research Hub
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Are you reporting your data in median and ranges if your numerical variables didn't fulfill the parametric assumptions (as known as not normally distributed data)
Well, in fact … Mann-Whitney -Wilcoxon rank-sum uses the rank of each case

The main calculation of Mann-Whitney-Wilcoxon rank-sum test has nothing to do with medians. The rank sum test is ineffective as a generic test of medians. Without a doubt, the null hypothesis cannot be said to be rejected because of difference in medians
So …. What should you do , I used to report also the pseudo-median , and when I explain to my clients or reviewers that the Wilcoxon uses the mean sum of ranks from the observations

Actually, if you are using R software , you will find it normally generated by the Hodges-Lehmann estimator when calling the Wilcoxon test in R
Also you may consider using the wilcox.conf: , Confidence Functions for the (Pseudo)Median or Shift
Confidence functions for the (pseudo)median of a continuous distribution via the Wilcoxon signed-rank test (for one sample) or shift between two continuous distributions via the Wilcoxon rank-sum test (for two samples).
Don't forget to edit the argument inside the arguments to match your purpose whether you are testing one sample against population parameters 2 samples or paired samples