DHT: A nonparametric test for homogeneity of multivariate dispersions

Music City Center 

Testing homogeneity across groups in multivariate data is often a standalone scientific question as well as an auxiliary step in verifying assumptions of ANOVA. Existing methods either construct test statistics based on distance of each observation from the group center, or mean of pairwise dissimilarity of the data points in a group. Both approaches can fail when mean within-group distance is similar across groups but the distribution of the within-group distances are different. This is a pertinent question in high dimensional microbiome data, where outliers and overdispersion can distort the performance of a mean-dissimilarity based test. We introduce a non-parametric Distance based Homogeneity Test (DHT) which combines information provided by Kolmogorov Smirnov as well as Wasserstein distance between the within-group dissimilarities for each pair of groups. Pairwise group tests are combined in the subsequent step to provide a permutation based p-value. Through simulations we show that our method has higher power than existing tests for homogeneity in certain situations. We also provide a general framework for extending the test to a continuous covariate.

permutation tests

ANOVA

multivariate tests

nonparametric

Wasserstein Distance

Kolmogorov-Smirnov 

Section on Statistics in Genomics and Genetics