If X1, X2, . . ., Xn1 and Y1, Y2, . . ., Yn2 are independent random samples, we can test the null hypothesis that they come from identical continuous populations on the basis of the Mann-Whitney statistic U, which is simply the number of pairs (xi, yj) for which xi > yj. Symbolically,

Where

For i = 1, 2, . . . , n1 and j = 1, 2, . . . , n2. Show that this Mann-Whitney U statistic is the same as the U1 statistic of Section 16.4.

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ni n2