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I never took a statistical class, but I had one in probabilities. Calculate the average and the standard deviation for both X and Y. With average and the stdev you can plot a gaussian random variable for, lets say gX (for X) and gY (for Y).
The next step is something to do with ln, and then division and subtraction, and than an integration. But it is late and I cant remember. In the end you get the probability (between 0 and 1) that X is greater than Y.
I did this once in a research paper comparing the predicted resistance to the tested resistance of deep pile foundaitons. (When the predicted resistance is greater than the tested load capacity, then designed foundations could fail. The point was to evaluate the reliability of various prediction methods).
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