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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.

Bernd Weiss
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Mog
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1 Answers1

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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

Harvey Motulsky
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    This is a much more informative answer. +1 – Mark Ramotowski Apr 23 '14 at 11:07
  • 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 – rep_ho Jan 20 '20 at 20:38