  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.
