# Why is the Mann–Whitney U test significant when the medians are equal?

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.

• Thanks again @Bernd. I thought I'd searched for this answer, but clearly I missed it! Cheers!
– Mog
May 21, 2011 at 17:40
• +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, 2011 at 20:04
• @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. May 21, 2011 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. May 21, 2011 at 23:32
• 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. 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.