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DHT: A nonparametric test for homogeneity of multivariate dispersions

Abstract Number:

1411 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Asmita Roy (1), ni Zhao (2), Glen Satten (3)

Institutions:

(1) Johns Hopkins University School of Public Health, N/A, (2) Johns Hopkins University, N/A, (3) Emory University School of Medicine, N/A

Co-Author(s):

ni Zhao  
Johns Hopkins University
Glen Satten  
Emory University School of Medicine

First Author:

Asmita Roy  
Johns Hopkins University School of Public Health

Presenting Author:

Asmita Roy  
Johns Hopkins University School of Public Health

Abstract Text:

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.

Keywords:

permutation tests|ANOVA|multivariate tests|nonparametric|Wasserstein Distance|Kolmogorov-Smirnov

Sponsors:

Section on Statistics in Genomics and Genetics

Tracks:

Miscellaneous

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