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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.

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2 Answers

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

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Thanks again @Bernd. I thought I'd searched for this answer, but clearly I missed it! Cheers! – Mog May 21 '11 at 17:40
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+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? ;-) – whuber♦ May 21 '11 at 20:04
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@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. – cardinal May 21 '11 at 22:49
@whuber For example in sociology. And I am guilty too. It took me some time to understand how the test actually works. – Bernd Weiss May 21 '11 at 23:32
@cardinal Which statistical software package do you mean? – Bernd Weiss May 21 '11 at 23:34
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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

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