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The Mann-Whitney U-test is used to test whether two independent samples of observations are drawn from the same or identical distributions. An advantage with this test is that the two samples under consideration do not necessarily need to have the same number of observations or instances.
The KW Test is for the one factor case only. In the two factor case, we have limited options available. When one of the two factors is a blocking factor, the we can use Friedman's Test for a nonparametric Randomized Complete Block Design. With a factorial experiment with two (or more factors), I opt for a rank based method that works very well.