ABSTRACT
The principles of permutation and bootstrap tests can also be applied in the
case of more than two groups. In the simplest case of a completely randomized
design with k independent groups, the permutations are the possible alloca-
tions of the observations to the k groups. Possible test statistics include the
rank-based Kruskal-Wallis statistic and the F statistic of the one-way anal-
ysis of variance (ANOVA). By analogy with the two-sample Fisher-Pitman
permutation test (section 2.1) the F statistic can be computed for every per-
mutation, and the resulting permutation null distribution can be used for
inference instead of the F distribution. For this permutation test there are
other equivalent test statistics. For example, the mean square between the
groups, that is, the numerator of the F statistic, can be used as the test
statistic (Manly, 2007, p. 136).
