# Unequal Sample Size and Wilcoxon Rank Sum Test

It is my understanding that it is okay to perform the Wilcoxon Rank Sum test with slightly unequal sample sizes. I just don't understand how the Wilcoxon accounts for the missing numbers in one group given that it subtracts a random score of one group to a random score of another group.

Also, what would you say is the H1 of the wilcoxon rank sum test is? I've been seeing some different definitions in my readings.

• Please do not change your post to say thank you. We want your question to be around for future readers. – gung Dec 10 '15 at 0:01
• PaperRockBazooka: if you got a good answer somewhere else, the right thing to do would be to post an explanation of the answer you got, for the benefit of others. If an answer here solves your problem there are ways to indicate that. – Glen_b Dec 10 '15 at 0:36

There's not one single alternative for the Wilcoxon Rank Sum test; it depends on what additional assumptions you make and how you look at it. The most general alternative form is that $P(X>Y)\neq \frac12$ (two tailed; the one tailed versions replace $\neq$ with either $<$ or $>$).