DISCO analysis: A nonparametric extension of analysis of variance

TL;DR

DISCO analysis introduces a nonparametric extension of ANOVA using pairwise distances, enabling flexible hypothesis testing for equal distributions in univariate or multivariate data.

Contribution

It extends classical ANOVA by employing all pairwise distances and deriving a new decomposition for powers of distance in (0,2], providing a versatile nonparametric testing framework.

Findings

Provides a new nonparametric test for multi-sample equality of distributions.

Generalizes ANOVA F statistic to a broader class of distance powers.

Demonstrates statistical consistency against general alternatives.

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.