The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species richness and composition are of roughly similar importance for primary productivity in grassland biodiversity experiments.