A manova statistic is just as powerful as distance-based statistics, for multivariate abundances

There is now quite an extensive literature based on analysis of multivariate abundances, which have often been collected according to a MANOVA design. Many test statistics have been proposed specifically for this case, yet remarkably the power of these methods has not previously been compared. In this paper, the power of distance-based statistics (e.g., Mantel, analysis of similarities) is compared to variable-based statistics (e.g., redundancy analysis, the sum of ANOVA F statistics), when using permutation tests to assess significance of all statistics. Different choice of transformation, standardization, and distance measure were considered. For 19 data sets taken from the literature, P values for the different statistics were compared. Power simulations were then conducted, where data were generated to mimic the properties of each of the 19 data sets. For transformed data, using different distance measures (Euclidean, Manhattan, BrayCurtis) and different distance-based statistics had little effect on power. Overall, statistics based on multivariate analysis of variance (MANOVA) were at least as powerful as others, although particular data sets gave different results. The distance-based statistics most commonly used in the literature do not standardize abundances, so these were more powerful when effects are present in taxa that are more variable (on the transformed scale), and less powerful otherwise. There are several reasons to prefer a statistic based on MANOVA to others (e.g., interpretability, generalization to more complex designs), and so we generally recommend that the MANOVA-based statistics used here be preferred to distance-based statistics.