Disco Analysis: a Nonparametric Extension of Analysis of Variance

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.