ABSTRACT
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
H0 : F = G vs H1 : F = G, (8.1)
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 of multivariate independence
H0 : FX,Y = FXFY vs H1 : FX,Y = FXFY (8.2)
under the null hypothesis the data in a sample need not be matched, and all pairs of samples obtained by permutations of the row labels (observations) of either sample are equally likely. Any statistic that measures dependence can be applied in a permutation test.
