What is the difference between the Mann-Whitney and Wilcoxon rank-sumtest? 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?
 A: 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.
