DISCO analysis: A nonparametric extension of analysis of variance
Maria L. Rizzo, Gábor J. Székely
The Annals of Applied Statistics · 2010 · Volume 4 · Issue 2
Abstract
In classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in (0, 2]. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in (0, 2), this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent against general alternatives.
Keywords
DISCO, Distance components, multisample problem, multivariate, nonparametric MANOVA extension, test equal distributions
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