20

I have two unequal groups (94 and 52) and want to run a Mann-Whitney U-test to see whether their scores on a measured variable differ. I see that it is OK to do with Kruskall-Wallis, does the same apply to Mann-Whitney?

gung - Reinstate Monica
  • 132,789
  • 81
  • 357
  • 650
George
  • 243
  • 1
  • 2
  • 6
  • 3
    Mann-Whitney (comparing two groups) is only the special case of Kruskal-Wallis (more than two groups), so yes. – sitems Oct 13 '12 at 20:43

2 Answers2

21

Yes, the Mann-Whitney test works fine with unequal sample sizes.

Harvey Motulsky
  • 14,903
  • 11
  • 51
  • 98
  • Can you exposed a published reference for that? –  Jan 14 '13 at 04:35
  • 5
    @jorge Mann, Henry B.; Whitney, Donald R. (1947). "[On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other](http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoms/1177730491)". Annals of Mathematical Statistics 18 (1): 50–60. --- the purpose of the original paper was to derive the distribution for two samples of different size, and show its consistency and asymptotic normality as well as giving the exact distribution for small samples. – Glen_b Jan 14 '13 at 11:49
16

@HarveyMotulsky is right, you can use the Mann-Whitney U-test with unequal sample sizes. Note however, that your statistical power (i.e., the ability to detect a difference that really is there) will diminish as the group sizes become more unequal. For an example, I have a simulation (actually of a t-test, but the principle is the same) that demonstrates this here.

Community
  • 1
gung - Reinstate Monica
  • 132,789
  • 81
  • 357
  • 650
  • 2
    Indeed, the analogy with the $t$ is quite direct, since the Mann-Whitney statistic is monotonic function of a t-statistic computed on the ranks. The precision of a difference in population means in the t-test is a simple function of $n_1$ and $n_2$ (*ceteris paribus*), and the same thing applies to the Mann-Whitney in respect of the difference in expected mean rank for the two samples. The same apt analogy with area that you mention in your linked answer applies here in the sense of maximizing the precision of that difference. – Glen_b Sep 18 '13 at 01:37