A comparison of the Mantel test with a generalised distance covariance test

The Mantel test based on a comparison of two distance matrices belongs to standard statistical tools for assessing an association between two sets of variables. Even though it has been widely used in biological, ecological and related studies, several objective criticisms have appeared recently in the methodological literature. In this paper, we compare the Mantel test with a generalisation of a recently introduced concept of distance covariance (dCov). This generalisation, denoted further as dCovG, keeps the simplicity of the Mantel test, but at the same time, it is more flexible and might be advantageous in applications. The dCovG test includes the RV coefficient as well as dCov as two important special cases. Furthermore, we show the link of dCovG test with PROTEST, a multivariate correlation coefficient, canonical correlations and redundancy analysis. A simulation study compares the power of the dCovG test with the Mantel test and PROTEST. The benefits of the dCovG test are illustrated by a real data analysis as well. Copyright © 2013 John Wiley & Sons, Ltd.