A new method for non-parametric multivariate analysis of variance

Hypothesis-testing methods for multivariate data are needed to make rigorou s probability statements about the effects of factors and their interaction s in experiments. Analysis of variance is particularly powerful for the ana lysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate dat a sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps mor e intuitive formulation for ANOVA (based on sums of squared distances) to c omplement the description provided by McArdle and Anderson (in press) for t he analysis of any linear model. It is an improvement on previous non-param etric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lac k of formal assumptions of other non-parametric methods. The test-statistic is a multivariate analogue to Fisher's F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obta ined using permutations. Some examples of the method are given for tests in volving several factors, including factorial and hierarchical (nested) desi gns and tests of interactions.