Randomization tests
APL '74 Proceedings of the sixth international conference on APL
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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,...,Kn are iid Bernoulli [1/2] and a1,...,an are 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-1 in 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.