## Exact permutation/randomization tests algorithms.(English)Zbl 1458.62159

Summary: R. A. Fisher [The design of experiments. Edinburgh, London: Oliver & Boyd (1937; JFM 61.0566.03)] described the exact permutation and randomization tests for comparative experiments without assuming normality or any particular probability distribution (see also [R. A. Fisher, Statistical methods, experimental design and scientific inference. A re-issue of ‘Statistical methods for research workers’, ‘The design of experiments’, and ‘Statistical methods and scientific inference’. Ed. by J. H. Bennett. With a foreword by F. Yates. Oxford: Oxford University Press (1990; Zbl 0705.62003)]). While having this as an attractive feature, the computational challenge was a disadvantage at that time but not now with modern computers. This paper introduces a permutation/randomization data algorithm to generate the permutation/randomization distributions under the null hypotheses for calculating the $$P$$-values. The properties of permutation/randomization data matrices developed by algorithms following the proposed mathematical processes are derived. Two illustrative examples demonstrate the usefulness of the proposed computational methods.

### MSC:

 62K10 Statistical block designs 62G10 Nonparametric hypothesis testing 62-08 Computational methods for problems pertaining to statistics

### Citations:

Zbl 0705.62003; JFM 61.0566.03
Full Text:

### References:

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