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Testing for Homogeneity of Multivariate Dispersions Using Dissimilarity Measures
Author(s) -
Gijbels Irène,
Omelka Marek
Publication year - 2013
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2012.01797.x
Subject(s) - homogeneity (statistics) , pairwise comparison , statistic , multivariate statistics , sample size determination , mathematics , statistics , distance matrices in phylogeny , statistical hypothesis testing , parametric statistics , inference , test statistic , type i and type ii errors , permutation (music) , computer science , artificial intelligence , combinatorics , physics , acoustics
Summary Testing homogeneity of dispersions may be of its own scientific interest as well as an important auxiliary step verifying assumptions of a main analysis. The problem is that many biological and ecological data are highly skewed and zero‐inflated. Also the number of variables often exceeds the sample size. Thus data analysts often do not rely on parametric assumptions, but use a particular dissimilarity measure to calculate a matrix of pairwise differences. This matrix is then the basis for further statistical inference. Anderson (2006) proposed a distance‐based test of homogeneity of multivariate dispersions for a one‐way ANOVA design, for which a matrix of pairwise dissimilarities can be taken as an input. The key idea, like in Levene's test, is to replace each observation with its distance to an estimated group center. In this paper we suggest an alternative approach that is based on the means of within‐group distances and does not require group centre calculations to obtain the test statistic. We show that this approach can have theoretical as well as practical advantages. A permutation procedure that gives type I error close to the prescribed value even in small samples is described.