# Wilcoxon-Mann-Whitney test for two independent samples

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. So I don't quite get why the test can be used if the data is "merely" of ordinal scale? How is the test statistic derived in this case? I couldn't really find a proper source explaining me my problem, so could anyone recommend me a good book,script etc. or explain briefly why the test works on ordinal data ?

Thank you!