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I compared two unequal sized samples, N1 = 108297 and N2 = 72922 using a Mann-Whitney U test. The U is shown to be large such as 7.37 e+8.

And p value is < 0.001. I am just wondering that such large U value is ok. Or is there something wrong there? I am using R software.

Daniel
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    I see nothing to worry about. With such large sample sizes, you're almost guaranteed to find something "significant" because you have huge statistical power. So yes, such a large U is okay. – COOLSerdash Aug 14 '23 at 05:40
  • Ok so large U value with significant p value has shown positive impact impact for my result.? – Daniel Aug 14 '23 at 06:29
  • You haven't said anything about your actual data and hypothesis you want to test. The MWU-test tests a specific null hypothesis not related to means or medians. The Wikipedia article goes into detail about this. – COOLSerdash Aug 14 '23 at 07:18

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Given that the test statistic is built as a function of the sum of the orders of one of the samples, it will correspond at most to n1n2+n2(n2+1)/2-sum(1:n2) or which for your sample sizes is 7897233834, higher than your observed test statistic, so in that sense the value reported could be correct, and indeed will be correct if you used the right syntax. However the true question to ask is what are you trying to achieve with your test? With the sample size that you are considering any real difference will be statistically significant, but that statement in itself is meaningless (check e.g. Moving to a World Beyond “p < 0.05” by Wasserstein, Schirm & Lazar), it just means you have huge sample sizes. You might want to focus on whether the observed difference is meaningful at all in the context you are working under. Note something that look much this has actually been answered before: Mann-Whitney U test with very large sample size?

Tiago Marques
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