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I am looking to determine whether two medians are not equal and attempt to estimate the median difference between the two. From my research, I have found this can be done by performing the Wilcoxon Mann u test and quantile regression. However, I am confused on interrupting the for results each. Below if my data, code for both, results, and interpretation.

I think I am in the right direction but, having trouble with the median difference estimate interpretation for a write up. Is how I described the MannU appropriate? I believe I understand that it is not a test of median difference but whether they are not equal.

Happy to clarify anything that may have been unclear and appreciate the support. Using SAS, npar1way and proc quantreg.

Mann U (npar1way) median a median b median diff pval (kruskalW) hodgeL Interpretation 601 642 41 0.01 issue getting to load Median A and Median B are considered to be significantly different (difference=41, p<.05) as determined by the mannU test Quantile regression median a median b median diff pval Interpretation 601 642 34 (-74 - 143.78) 0.524 Median A and Median B are not considered to be significantly different (difference= 34.5 (-74.7 - 143.78), p=.52) as determined by quantile regression

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Simply, the Wilcoxon-Mann-Whitney test is not in general a test of medians. If you want to test the medians, you can use quantile regression, Mood's median test, or an appropriate permutation test.

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