A statistical test and sample size recommendations for comparing community composition following PCA

Many investigations of anthropogenic and natural impacts in ecological systems attempt to detect differences in ecological variables or community composition. Frequently, ordination procedures such as principal components analysis (PCA) or canonical correspondence analysis (CCA) are used to simplify such complex data sets into a set of primary factors that express the variation across the original variables. Scatterplots of the first and second principal components are then used to visually inspect for differences in community composition between treatment groups. We present a multidimensional extension of analysis of variance based on an analysis of distance (ANODIS) that can be used to formally test for differences in community composition using 1, 2, or more dimensions of a PCA or CCA of the original sample observations. The statistical tests of significance are based on F-statistics adapted for the analysis of this multidimensional data. Because the analysis is parametric, power and sample size calculations useful in the design of field studies can be readily computed. The use of ANODIS is illustrated using bivariate PCA scatterplots from three published studies. Statistical power calculations using the noncentral F-distribution are illustrated.