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Under the null hypothesis of independency, the exact mean and variance of Wald and Wolfwitz statistic W_N are calculated. For the case of equally likely permutations, tables of the exact distribution of W are given for 6 <___- N <___- 13 and Monte Carlo approximate results are given for 14 <___- N <___- 30. The simple normal approximation may be adequate for N >___- 31. Some properties of W_N are given and a serial correlation test based on W_N is applied to a small-sample example.
