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I have this written down on a piece of paper in my office. I will bring it home tommorow. From what I remember, the integral could not be solved analytically. So a numerical approximation is used at the end, probably gaussian quadrature. And sample size is irrelevent. All that is reqruied is the mean and standard deviation.
The biggest assumption is that the data will comply to a gaussian random variable. This is applicable for people heights, etc... However, it is not applicable for linear reandom (like rolling a dice).
And another thing, the result is not a test that X > Y. It is the probability that if you sampled X and Y one more time, the X result would be greater than the Y.
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