Efficient calculation of p-values in linear-statistic permutation significance tests

Abstract

It is shown that the exact p-values of permutation and bootstrap hypothesis tests of difference between groups can be written as an infinite series whose terms can be computed rapidly, even for large group sizes. Because of connections with the N-step random walk in the plane, the rate of convergence of the series improves as the size of the resampling distribution increases.

Keywords:

• Hypothesis tests
• Permutation
• Randomization
• Bootstrap
• Significance level

Acknowledgements

I thank Dr Malcolm Gill for suggesting this problem to me, Dr Andrew Gilbert for useful discussions and Prof. Andy Wood and Dr Michael Martin for helpful suggestions concerning this manuscript.

Additional information

Notes on contributors

Peter M. W. Gill

Email: [email protected]