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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!

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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.

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    $\begingroup$ The carefully worded last paragraph usually bites hard. You really need independent evidence on distribution shapes. $\endgroup$ – Nick Cox Mar 16 '15 at 15:33
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    $\begingroup$ Thank you (+1)! I think the "cross-group" was an important point. Usually pairwise would suggest "pairs of observations" which is not a requirement for MW as it is still applicable when dealing with unequal sample sizes. $\endgroup$ – usεr11852 says Reinstate Monic Jul 30 at 22:55
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Eric, I don't know if you solved your problem but I think the approach of the asterisk is ok. If you think the means represent better the data behavior than just use them. Check the CV%, it can also give a perspective of the dispersion which can be important.

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