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arXiv · 1011.2288

DISCO analysis: A nonparametric extension of analysis of variance

Maria L. Rizzo·Gábor J. Székely
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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.

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Maria L. Rizzo, Gábor J. Székely. 2010-11-10. DISCO analysis: A nonparametric extension of analysis of variance. https://doi.org/10.1214/09-aoas245

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