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      Distance-based tests for homogeneity of multivariate dispersions.

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      Biometrics
      Wiley

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          Abstract

          The traditional likelihood-based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero-inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non-Euclidean dissimilarity would be more appropriate. Distance-based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene's test, with P-values obtained either using the traditional F-distribution or using permutation of either least-squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Niño. Monte Carlo simulations from the real data sets show that the distance-based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.

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          Author and article information

          Journal
          Biometrics
          Biometrics
          Wiley
          0006-341X
          0006-341X
          Mar 2006
          : 62
          : 1
          Affiliations
          [1 ] Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand. mja@stat.auckland.ac.nz
          Article
          BIOM440
          10.1111/j.1541-0420.2005.00440.x
          16542252
          8b7075d0-e5df-4b7a-a6c7-85e684462475
          History

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