Exact nonparametrics in APL

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Abstract
The authors present a new algorithm for the exact distribution of many nonparametric tests. The algorithm is based on a recursion formula that relates the distribution of where K1,...,Knare iid Bernoulli [1/2] and a1,...,anare fixed p-vectors, to the distribution of Tn-1. The core idea is to realize this recursion by shifts of the p - dimensional distribution of Tn-1in the computer main storage, which can be implemented efficiently in APL. We believe, that the method has achieved a breakthrough in the practical application of Fisher-Pitman permutation tests, but it can also be used routinely in the computation of many other tests by applying an initial transformation to the original data. A noteworthy example is the Wilcoxon test with arbitrary ties in the data, whose exact distribution can easily be computed for Nample 100.In order to allow the direct use of these results, a complete list of the necessary APL programmes is included in the text.

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