Statistical Computing with R

Chapter 8

Permutation Tests

8.1 Introduction

Permutation tests are based on resampling, but unlike the ordinary bootstrap, the samples are drawn without replacement. Permutation tests are often applied as a nonparametric test of the general hypothesis

$\begin{array}{cc}{H}_0:F=Gvs{H}_1:F\ne G,& \left(8.1\right)\end{array}$

where F and G are two unspecified distributions. Under the null hypothesis, two samples from F and G, and the pooled sample, are all random samples from the same distribution F. Replicates of a two sample test statistic that compares the distributions are generated by resampling without replacement from the pooled sample. Nonparametric tests of independence, association, location, common scale, etc. can also be implemented as permutation tests. For example, in a test ...