# Applications of conditional power function of two-sample permutation test

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## Abstract

Permutation or randomization test is a nonparametric test in which the null distribution (distribution under the null hypothesis of no relationship or no effect) of the test statistic is attained by calculating the values of the test statistic overall permutations (or by considering a large number of random permutation) of the observed dataset. The power of permutation test evaluated based on the observed dataset is called *conditional power*. In this paper, the conditional power of permutation tests is reviewed. The use of the conditional power function for sample size estimation is investigated. Moreover, reproducibility and generalizability probabilities are defined. The use of these probabilities for sample size adjustment is shown. Finally, an illustration example is used.

## Keywords

Generalizability probability Permutation test Reproducibility probability Sample size adjustment Sample size estimation## Notes

### Acknowledgements

The authors would like to thank the associated editor and referees for their comments that contribute in improving the paper. We also greatly appreciate Dr. Ibrahim Almasri, Department of Applied Mathematics and Physics - Palestine Polytechnic University, for being kind enough to read and improve the language of the paper.

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