I have two samples x=[7,6,4] and y=[5,9] and I want to test the hypothesis of them having equal means versus the hypothesis that the distribution of y being stochastically larger than the distribution of x, using a permutation test. The empirical distribution functions suggest that y is stochastically larger than x but it is very close. I am supposed to use the test statistic T=mean(y)-mean(x). How would this test statistic contain information about whether Y is stochastically larger than X or not?
Thanks in advance.