Derivation of the Test Statistic for the Mann-Whitney U Test

Students often confuse the rank-sum

R_1

with the

U

statistic itself, or fail to realize that

U_1

and

U_2

are perfectly symmetric such that

U_1 + U_2 = n_1 n_2

. Forgetting the triangular number correction for the minimum rank is another common calculation pitfall.

Institutional Reference: Applied Statistics