First of all, what is the difference between the Mann-Whitney and Wilcoxon rank-sum test? How do I choose between the two? I know the latter is implemented in R, is there a way to do the Mann-Whitney test? Is there a way I can include my (very large) datasets in this post so you can get an idea of what I'm trying to do?
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How are the particular datasets you are working with relevant to your questions? You are asking questions that don't depend on anyone's data. – Nick Cox Sep 01 '14 at 09:46
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A search for "Wilcoxon Mann Whitney" on this forum yielded 158 results. I suggest that you need to search for an answer before you can be sure that you have a new question. – Nick Cox Sep 01 '14 at 09:48
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I did quite a bit of reading and have an idea about it. Actually, I wanted to post the datasets so it's easier to see what I'm talking about, but they're too big to post here and I don't see an option to attach a file. – Stefan Sep 01 '14 at 09:51
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Your question is comprehensively dealt with in the R help for `wilcox.test`. – Glen_b Sep 01 '14 at 09:53
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First of all it might be useful to remember that Mann-Whitney test is also called Wilcoxon rank-sum test. Since it is the same test there is no need to explain the difference ;) A good answer to the common question about the difference between W statistic and U statistic is given here: Is the W statistic output by wilcox.test() in R the same as the U statistic?
Mann-Whitney/Wilcoxon rank-sum test (later MWW test) is defined in R through function wilcox.test (with paired=FALSE) which uses [dprq]wilcox functions.
However, people sometimes mistake MWW with Wilcoxon signed-rank test.
The difference comes from the assumptions. In the MWW test you are interested in the difference between two independent populations (null hypothesis: the same, alternative: there is a difference) while in Wilcoxon signed-rank test you are interested in testing the same hypothesis but with paired/matched samples.
For example, the Wilcoxon signed-rank test would be used if you had replicates (repeated) measurements between different time points/plates/... since it is the same sample but measured in different time/on different plates.
Wilcoxon signed-rank test is defined in R through wilcox.test function (with paired=TRUE) which uses [dprq]signrank functions.
Another implementation of MWW/Wilcoxon signed-rank test can be found in the coin package through wilcox_test function.
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Thanks for the input iugrina, If I may ask a couple of more questions - the Mann-Whitney U test outputs a U value. In R I get a W value. Is that the U value or is it a different metric? If so, what is W? – Stefan Sep 01 '14 at 09:54
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You should take a look at this question: http://stats.stackexchange.com/questions/79843/is-the-w-statistic-outputted-by-wilcox-test-in-r-the-same-as-the-u-statistic – iugrina Sep 01 '14 at 10:24
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@user3790338 I recommend reading the original articles by Wilcoxon and by Mann and Whitney, also. – Alexis Sep 01 '14 at 15:48
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