Abstract
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.
Highlights
Multivariate analysis is often exploratory or descriptive rather than inferential in nature
We present a multidimensional extension of analysis of variance based on an analysis of distance (ANODIS) that can be used to test for differences in community composition using 1, 2, or more dimensions of a principal components analysis (PCA) or correspondence analysis (CCA) of the original sample observations
The property of independence allows the analysis of the separate components to be combined based on the principle that the sum of independent chi-square statistics is chi-square distributed with degrees of freedom equal to the sum of the separate degrees of freedom
Summary
Multivariate analysis is often exploratory or descriptive rather than inferential in nature. Overparameterization of the information forces investigators to use post hoc methods such as cluster analysis, principal components analysis (PCA), or canonical correspondence analysis (CCA) to summarize and simplify the sample comparisons. Ordination procedures such as PCA offer a systematic way to reduce dimensionality of complex data sets and organize it into new independent composite variables (i.e., the principal components). Redundancy in the data set is minimized and sampling entities are organized around a few important gradients, which aid descriptive interpretation [1,2,3]. It eliminates concern over bias due to linearly
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