# Fast approximation of small p‐values in permutation tests by partitioning the permutations

Fast approximation of small p‐values in permutation tests by partitioning the permutations Introduction and MotivationMany researchers in the life sciences use permutation tests, for example, to test for differential gene expression (Doerge and Churchill, ; Morley et al., ; Stranger et al., , ; Raj et al., ), and to analyze brain images (Nichols and Holmes, ; Bartra et al., ; Simpson et al., ). These tests are useful when the sample size is too small for large sample theory to apply, or when the distribution of the test statistic is analytically intractable. Permutation tests are also exact, meaning that they control the type I error rate exactly for finite sample size (Lehmann and Romano, ). However, permutation tests can be computationally intensive, especially when estimating small p‐values for many tests. In this article, we present computationally efficient methods for approximating small permutation p‐values (e.g., <10−6) for the difference and ratio of means in two‐sample tests, though we speculate that our methods will also work for other smooth function of the means.We denote the two groups of sample data as x=(x1,…,xnx)′ and y=(y1,…,yny)′, with respective sample sizes nx and ny. We denote the full data as z=(x′,y′)′, with total sample size N=nx+ny. Writing z=(z1,…,zN)′, we have that zi=xi,i=1,…,nx, and znx+j=yj,j=1,…,ny. In http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrics Wiley

# Fast approximation of small p‐values in permutation tests by partitioning the permutations

, Volume 74 (1) – Jan 1, 2018
11 pages

/lp/wiley/fast-approximation-of-small-p-values-in-permutation-tests-by-H0I4SSLC69
Publisher
Wiley Subscription Services, Inc., A Wiley Company
© 2018, The International Biometric Society
ISSN
0006-341X
eISSN
1541-0420
D.O.I.
10.1111/biom.12731
Publisher site
See Article on Publisher Site

### Abstract

Introduction and MotivationMany researchers in the life sciences use permutation tests, for example, to test for differential gene expression (Doerge and Churchill, ; Morley et al., ; Stranger et al., , ; Raj et al., ), and to analyze brain images (Nichols and Holmes, ; Bartra et al., ; Simpson et al., ). These tests are useful when the sample size is too small for large sample theory to apply, or when the distribution of the test statistic is analytically intractable. Permutation tests are also exact, meaning that they control the type I error rate exactly for finite sample size (Lehmann and Romano, ). However, permutation tests can be computationally intensive, especially when estimating small p‐values for many tests. In this article, we present computationally efficient methods for approximating small permutation p‐values (e.g., <10−6) for the difference and ratio of means in two‐sample tests, though we speculate that our methods will also work for other smooth function of the means.We denote the two groups of sample data as x=(x1,…,xnx)′ and y=(y1,…,yny)′, with respective sample sizes nx and ny. We denote the full data as z=(x′,y′)′, with total sample size N=nx+ny. Writing z=(z1,…,zN)′, we have that zi=xi,i=1,…,nx, and znx+j=yj,j=1,…,ny. In

### Journal

BiometricsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ;

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