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June 2010 DISCO analysis: A nonparametric extension of analysis of variance
Maria L. Rizzo, Gábor J. Székely
Ann. Appl. Stat. 4(2): 1034-1055 (June 2010). DOI: 10.1214/09-AOAS245


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. "DISCO analysis: A nonparametric extension of analysis of variance." Ann. Appl. Stat. 4 (2) 1034 - 1055, June 2010.


Published: June 2010
First available in Project Euclid: 3 August 2010

zbMATH: 1194.62054
MathSciNet: MR2758432
Digital Object Identifier: 10.1214/09-AOAS245

Keywords: DISCO , Distance components , multisample problem , multivariate , nonparametric MANOVA extension , test equal distributions

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.4 • No. 2 • June 2010
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