Quick test for comparing two populations with bivariate data.

A simple nonparametric test is given for testing the equality of two populations when the observations (X, Y) are bivariate and the alternative of interest is that the conditional c.d.f. of Y given X for one population dominates that for the other for every value of X. The procedure consists of fitting a curve through the combined set of data points and considering and conditional distribution of the number of points above the curve from one population, given certain information (depending on the design of the experiment), on the combined set of data. When used to compare two bivariate distributions, the test reduces to Fisher's exact test for 2 X 2 tables.