DTH: a nonparametric test for homogeneity of multivariate dispersions

Testing for differences in within-group dispersion is a fundamental problem in multivariate data analysis, with direct implications for interpreting group structure and validating statistical assumptions of other analysis such as ANOVA. Existing methods typically construct test statistics either based on the distance of each observation from the group center or on the mean of pairwise dissimilarities among observations within a group. Both approaches can fail when the mean within-group distance is similar across groups but the distributions of the within-group distances differ. This issue is particularly relevant in high-dimensional microbiome data, where outliers and overdispersion can distort the performance of mean-dissimilarity-based tests.

We introduce the non-parametric Distance-based Test for Homogeneity (DTH), which measures dispersion of a group by computing within-group dissimilarity. Difference in dispersion across groups is tested by comparing the distributions of the within-group dissimilarity across different groups. A combination of Kolmogorov-Smirnov and Wasserstein distances are used to construct the difference between the distributions. For more than two groups, pairwise group tests are combined using a permutation-based p-value. Through simulations, we show that our method has higher power than existing tests for homogeneity in certain situations and comparable power in others. For continuous covariates, we offer an heuristic extension of DTH that showed good performance in simulations.

The DTH package, along with the code for reproducing all simulations, analyses, and an accompanying vignette, is available at https://github.com/asmita112358/DTH.