Suppose that observations X1, X2, . . . , Xn are made on a process at times 1, 2, . . . , n. On the basis of this data, we wish to test H0: the Xis constitute an independent and identically distributed sequence versus Ha: Xi1 tends to be larger than Xi for i
1, . . . , n

(an increasing trend)

Suppose the Xis are ranked from 1 to n. Then when Ha is true, larger ranks tend to occur later in the sequence, whereas if H0 is true, large and small ranks tend to be mixed together. Let Ri be the rank of Xi and consider the