# Wilcoxon-Rank-Test for two independent samples

by ANew   Last Updated April 15, 2019 10:20 AM

This is my first question on this side, so please don't mind if not everything is correct :)

I'm currently trying to understand the Wilcoxon-Rank-Test/Mann-Whitney-Wilcoxon Test, but it got me kind of confused. As far as I understood it is to test whether the null hypothesis $$F_X = F_Y$$ can be rejected at level $$\alpha$$, where $$F_X$$ is the cumulative distribution of the random variable X and same for Y.

Now here's the problem: Mostly it is assumed that the cumulative distributions are continuous. The test statistic, the distribution of the rank vector and so on are derived based on that assumption. In case the cumulative distribution are not continuous I don't know why we apparently can get the same statistics. I hope what I've been telling was right, I'm just very confused at this point. My question here is if anyone has a good source which can help me understand my problem, since I didnt find any proper sources. Or maybe anyone could briefly explain how the test statistic is derived when we have continuous data or ordinal data.

Thank you!

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