Ecological applications of multilevel analysis of variance

A Bayesian representation of the analysis of variance by A. Gelman is introduced with ecological examples. These examples demonstrate typical situations encountered in ecological studies. Compared to conventional methods, the multilevel approach is more flexible in model formulation, easier to set up, and easier to present. Because the emphasis is on estimation, multilevel models are more informative than the results from a significance test. The improved capacity is largely due to the changed computation methods. In our examples, we show that ( 1) the multilevel model is able to discern a treatment effect that is smaller than the conventional approach can detect, ( 2) the graphical presentation associated with the multilevel method is more informative, and ( 3) the multilevel model can incorporate all sources of uncertainty to accurately describe the true relationship between the outcome and potential predictors.