The ranking procedure described in Exercise 35 is somewhat asymmetric, because the smallest observation receives rank 1 whereas the largest receives rank 2, and so on.

Suppose both the smallest and the largest receive rank 1, the second smallest and second largest receive rank 2, and so on, and let W, be the sum of the X ranks. The null distribution of W, is not identical to the null distribution of W, so different tables are needed. Consider the case m
3, n
4.