ON THE PERMUTATION DISTRIBUTION OF THE RANK PRODUCT-MOMENT STATISTIC

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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.