W_d^* -test: robust distance-based multivariate analysis of variance

Background Community-wide analyses provide an essential means for evaluation of the effect of interventions or design variables on the composition of the microbiome. Applications of these analyses are omnipresent in microbiome literature, yet some of their statistical properties have not been tested for robustness towards common features of microbiome data. Recently, it has been reported that PERMANOVA can yield wrong results in the presence of heteroscedasticity and unbalanced sample sizes. Findings We develop a method for multivariate analysis of variance, W_d^* , based on Welch MANOVA that is robust to heteroscedasticity in the data. We do so by extending a previously reported method that does the same for two-level independent factor variables. Our approach can accommodate multi-level factors, stratification, and multiple post hoc testing scenarios. An R language implementation of the method is available at https://github.com/alekseyenko/WdStar . Conclusion Our method resolves potential for confounding of location and dispersion effects in multivariate analyses by explicitly accounting for the differences in multivariate dispersion in the data tested. The methods based on W_d^* have general applicability in microbiome and other ‘omics data analyses.