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I already have calculated the U-Value of the Wilcoxon-Mann-Whitney-U test, and now I want to compare it against the critical value. However, all statistical tables I have found in various books or along the internet only have critical values for a sample size of max. 40. The sample size I have is 42 for population 1 and 10 for population 2 - how do I compute the critical value for that sample combination?

As my U-Value is much larger than the critical value given for sample sizes 40 / 10, I already can conclude that I cannot drop the H_0 Hypothesis. However, it would look much nicer if I could give the reader the exact critical value I have compared against.

The information on wikipedia tends to even confuse me more :)

Any hint will be highly appreciated. Thanks a lot.

Regenschein
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1 Answers1

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You could use the normal approximation, or you could use statistical software.

For example in R: 

> qwilcox(p=c(0.005,0.01,0.025,0.05), m=42, n=10) - 1
[1] 100 110 125 138

To compare this with whatever table you are looking at, for sample sizes of $20$ and $10$, the numbers would be 

> qwilcox(p=c(0.005,0.01,0.025,0.05), m=20, n=10) - 1
[1] 42 47 55 62

which are the same as, for example, those give in http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/mobile_pages/BS704_Nonparametric4.html or http://math.usask.ca/~laverty/S245/Tables/wmw.pdf

Henry
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