The Pseudo-Median
12th October 2022 By MARS Research Hub

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