ABSTRACT
When studying single variables in univariate statistics or pairs of variables in bivariate statistics, the testing of group differences and the study of pairwise variable relationships are fairly straightforward and well known, even when the variables might not be normally distributed. In the case of multivariate data when sample differences are measured by distance functions such as the χ2distance, possibly involving sample weighting, the theory becomes extremely complex. The concept of permutation testing has been known for a long time, but it is only with the advent of high-speed computing that they have come into their own as viable distribution-free methods for testing hypotheses using multivariate data. In this chapter we will look at several types of permutation tests that make it possible to draw statistical conclusions (inferences) in this more complex setting.
