Pairwise wilcoxon-mann-whitney?

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Is there something like a pairwise version of the wilcoxon-mann-whitney test, i.e. the version of the pairwise Wilcoxon signed rank test, but with alternative hypothesis?

I don't seem to be able to find any information on such a thing, neither on the web, nor in hypothesis testing handbooks.

Maybe there is no special paired version of the wmw and even if the data is paired, using wmw is fine...

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With pairwise data, you are typically testing hypotheses about the differences, correct? If so, the Wilcoxon signed rank test on the pairwise differences is a good test to use.