I've received a results from a Mann-Whitney rank test that I don't understand. The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are:

  1. 6.64 & 7.2
  2. 6.60 & 7.1

The p-value resulting from the test comparing these populations is 0.007. How can these populations be significantly different? Is it due to the spread about the median? A boxplot comparing the 2 shows that the second one has far more outliers than the first. Thanks for any suggestions.


2 Answers 2


FAQ: Why is the Mann-Whitney significant when the medians are equal?

  • $\begingroup$ Thanks again @Bernd. I thought I'd searched for this answer, but clearly I missed it! Cheers! $\endgroup$
    – Mog
    May 21, 2011 at 17:40
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    $\begingroup$ +1 It seems to be poorly known that the Wilcoxon/Mann-Whitney test is a test of medians only when there is purely a shift in distribution. This can be hard to get across to non-statisticians: in some fields, the M-W has become so popular that people assume it's always applicable. That's what "nonparametric" means, right? ;-) $\endgroup$
    – whuber
    May 21, 2011 at 20:04
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    $\begingroup$ @whuber, I've even seen at least one statistical software package where the Mann-Whitney test is there as an "alternative" to what is essentially a two-sample $t$-test with unequal variances. Ouch. $\endgroup$
    – cardinal
    May 21, 2011 at 22:49
  • $\begingroup$ @whuber For example in sociology. And I am guilty too. It took me some time to understand how the test actually works. $\endgroup$ May 21, 2011 at 23:32
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    $\begingroup$ It's really not good practice to just copy and paste links into CV answers. You should be explaining it, and then referencing your explanation. $\endgroup$ Apr 23, 2014 at 11:07

Here is a graph that shows the same point the FAQ Bernd linked to explains in detail. The two groups have equal medians but very different distributions. The P value from the Mann-Whitney test is tiny (0.0288), demonstrating that it doesn't really compare medians.

enter image description here

  • 2
    $\begingroup$ This is a much more informative answer. +1 $\endgroup$ Apr 23, 2014 at 11:07
  • $\begingroup$ should be noted that mann-whitney does not care about the distributions as they are, but about distribution of ranks, which is not as obvious from the image. MW is testing average rank, not median and why those are different can be seen in the figure $\endgroup$
    – rep_ho
    Jan 20, 2020 at 20:38

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