DISCO analysis: A nonparametric extension of analysis of variance
Open Access
- 1 June 2010
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Statistics
- Vol. 4 (2), 1034-1055
- https://doi.org/10.1214/09-aoas245
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
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