Permutation Tests and Nonparametric Combination Methodology

Abstract Motivation Permutation tests offer a straightforward framework to assess the significance of differences in sample statistics. A significant advantage of permutation tests are the relatively few assumptions about the distribution of the test statistic are needed, as they rely on the assumption of exchangeability of the group labels. They have great value, as they allow a sensitivity analysis to determine the extent to which the assumed broad sample distribution of the test statistic applies. However, in this situation, permutation tests are rarely applied because the running time of naïve implementations is too slow and grows exponentially with the sample size. Nevertheless, continued development in the 1980s introduced dynamic programming algorithms that compute exact permutation tests in polynomial time. Albeit this significant running time reduction, the exact test has not yet become one of the predominant statistical tests for medium sample size. Here, we propose a computational parallelization of one such dynamic programming-based permutation test, the Green algorithm, which makes the permutation test more attractive. Results Parallelization of the Green algorithm was found possible by non-trivial rearrangement of the structure of the algorithm. A speed-up—by orders of magnitude—is achievable by executing the parallelized algorithm on a GPU. We demonstrate that the execution time essentially becomes a non-issue for sample sizes, even as high as hundreds of samples. This improvement makes our method an attractive alternative to, e.g. the widely used asymptotic Mann-Whitney U-test. Availabilityand implementation In Python 3 code from the GitHub repository https://github.com/statisticalbiotechnology/parallelPermutationTest under an Apache 2.0 license. Supplementary information Supplementary data are available at Bioinformatics online.

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Robust permutation tests for two samples

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2008.12.003 ◽

2009 ◽

Vol 139 (8) ◽

pp. 2631-2642 ◽

Cited By ~ 3

Author(s):

Alan Huang ◽

Rungao Jin ◽

John Robinson

Keyword(s):

Permutation Tests ◽

Two Samples

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Permutation Tests for Common Locations Among Samples With Unequal Variances

Journal of Educational Statistics ◽

10.3102/10769986019003217 ◽

1994 ◽

Vol 19 (3) ◽

pp. 217-236 ◽

Cited By ~ 9

Author(s):

Paul W. Mielke ◽

Kenneth J. Berry

Keyword(s):

Null Hypothesis ◽

Treatment Effects ◽

Alternative Hypothesis ◽

Permutation Tests ◽

Experimental Designs ◽

Bivariate Distributions ◽

Unequal Variances ◽

Trace Test ◽

Location Shift ◽

Power Comparisons

In completely randomized experimental designs where population variances are equal under the null hypothesis, it is not uncommon to have multiplicative treatment effects that produce unequal variances under the alternative hypothesis. Permutation procedures are presented to test for (a) median location and scale shifts, (b) scale shifts only, and (c) mean location shifts only. Corresponding multivariate extensions are provided. Location-shift power comparisons between the parametric Bartlett-Nanda-Pillai trace test and three alternative multivariate permutation tests for five bivariate distributions are included.

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