Non-parametric multivariate analysis of variance: The use of permutation methods to overcome statistical roadblocks during analysis of entomological data sets

Hypothesis-testing methods for multivariate entomological data are needed to make rigorous probability statements about effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, can be too stringent in their assumptions for some entomological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This talk reviews a non-parametric method for multivariate analysis of variance and provides an intuitive introduction to this formulation for ANOVA (based on sums of squared distances) that applies to the analysis of any linear model. It is an improvement on earlier non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack 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 obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.