Prof. Marti J. Anderson1,5, Dr Daniel Walsh5, Prof. K. Robert Clarke2,4, Mr Ray N. Gorley4, Dr Edlin Guerra-Castro3
1PRIMER-e (Quest Research Limited), Auckland, New Zealand, 2Plymouth Marine Laboratory, Plymouth, United Kingdom, 3Universidad Nacional Autonoma de Mexico, Yucatan, Mexico, 4PRIMER-E Limited UK, Plymouth, United Kingdom, 5Massey University, Albany, Auckland, New Zealand
The Behrens‐Fisher problem is one of the oldest puzzles in statistics. The essence of this problem is how validly to compare means (or multivariate centroids) between two or more populations or groups when their variances (or multivariate dispersions) differ.
Ecologists often collect multivariate data (e.g., counts of abundances) and may use dissimilarity-based methods (such as ANOSIM or PERMANOVA) to test for differences among groups of samples in space or time, or in response to experimental treatments or changing environmental conditions. Usually, the goal is to test for differences in the mean (centroid) among groups, and to characterise those differences. However, these tests, like their classical counterparts, are sensitive to differences in within-group dispersions (variances/spread) among groups, particularly for unbalanced designs.
In this seminar, I will outline a robust solution to the multivariate Behrens-Fisher problem. Specifically, a modification of the PERMANOVA pseudo F-ratio can be used to test the null hypothesis of no differences among centroids, even when dispersions differ. The test is done in the space of a chosen dissimilarity measure, with a p-value obtained using either permutations or bootstrapping. It allows shifts in the centroid to be disentangled from dispersion effects in multivariate (or univariate) analyses. I’ll demonstrate the utility of this test for ecological inferences in the context of two examples: (i) large-scale differences in soft-sediment assemblages along the Norwegian continental shelf; and (ii) differences in diet composition of hatchery-reared vs wild salmonids from the U.S. Pacific Northwest.
Biography:
Distinguished Professor Marti J. Anderson (Massey University and PRIMER-e, Auckland, New Zealand) is an ecological statistician whose work spans several disciplines, from ecology to mathematical statistics. A Fellow of the Royal Society of New Zealand, she holds a Chair in Statistics in the New Zealand Institute for Advanced Study at Massey University, and her core research is in community ecology, biodiversity, multivariate analysis, experimental design and resampling methods, with a special focus on developing novel statistical methods for ecology.
