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**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 |

### Keywords:

block design; completely randomized design; hypothesis testing; paired data; permutation; randomization; randomized control trial; two-sample data
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\textit{S. Ghosh}, J. Stat. Theory Pract. 14, No. 4, Paper No. 65, 12 p. (2020; Zbl 1458.62159)

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### References:

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