# Using Wilcoxon-Mann-Whitney test for comparing two population of different sizes

I am using Wilcoxon-Mann-Whitney test for comparing two populations. Unfortunately, sizes of my population are different; one has size 100000 and the other 6000. Can I use this test to compare these populations? If not, is there any alternative test? Thanks!!

• Yes, you can do so. – David Robinson Mar 23 '14 at 14:32
• And I strongly advise you to study a nonparametric statistics text before proceeding. You would not have asked that question if you had had an introduction to nonparametric tests. – Frank Harrell Mar 23 '14 at 14:44
• I suppose you wanted to say "two samples", not "two populations". – ttnphns Mar 23 '14 at 15:35
• Hi, When I used Mann-Whitney-Wilcoxon (MWW) RankSum test of python(randalolson.com/2012/08/06/…), my p-value coming out 0.0. And hence I am accepting alternative hypothesis (i.e two samples are different). I just want to ask is it natural to get value 0.0. Thanks!! – Sangeeta Mar 23 '14 at 16:38
• The P value is not 0.00000000000.... It is simply smaller than the lowest fraction your program can print. – Harvey Motulsky Mar 23 '14 at 21:22

The size of the population should make no difference at all. But be very careful about whether you're confusing sample and population. The way you use them terms in comments makes me concerned you don't have them straight.

And hence I am accepting alternative hypothesis

You would more properly say 'reject the null' than 'accept the alternative'. You might conclude the alternative is the case, but the decision is simply to reject the null (or to fail to reject it).

(i.e two samples are different).

That the samples differ is generally obvious from inspection. You don't need hypothesis tests for that. Hypothesis tests are about populations, and we make inferences about them from the samples.

(However, in the case of permutation tests - of which the MWW is an example, the conclusions can be based on the assumption of random allocation, and needn't assume random sampling from populations -- but in the absence of random sampling the extension of the conclusions back to the population of interest may be more difficult, requiring an additional stage of argument.)

I just want to ask is it natural to get value 0.0.

The term 'natural' doesn't fit here. It's possible - even common - to get a value which is zero to many decimal places, and will show as zero to finite precision (and you shouldn't overly fuss about exactly what the value is in those circumstances).

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You should consider editing your question to clarify the circumstances.