Solved – Reporting Results of Mann-Whitney U Test – Means vs Medians

meanmedianordinal-datatableswilcoxon-mann-whitney-test

I had a question yesterday that I got a bunch of great responses on. I have, hopefully, a quicker question here.

There is a debate in the literature regarding reporting means vs medians in a Wilcoxon-Mann-Whitney test. See this and also this.

I would like to report means in my table, since I only have four possible values (0 through 3), rendering medians less effective as the differences are not pronounced. If I do report means in the table, would I just put an asterisk saying that means are reported for the Mann-Whitney test because the medians don't show the differences effectively? I feel like I need to explain why I used means and not medians to describe my ordinal data and show significance (even though a Mann-Whitney is comparing the distributions and not the medians, as some think).

Are there are any references out there that show this as a precedent? As always, advice/help is greatly appreciated!

Best Answer

The location-difference measure that the Mann-Whitney 'sees' is neither difference in means nor difference in medians -- it's the median of cross-group pairwise differences (the between samples quantity is the relevant estimate of the corresponding measure between populations).

See the end of this section of the wikipedia article on the Mann-Whitney (just above the section headed "Calculations").

The most typical additional assumptions required to make either the difference of means or medians reasonable (identity of distribution shapes is sufficient and is a commonly added assumption) immediately makes the other equally reasonable (at least assuming means are finite). So either: neither will be correct, or both should be good.