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.

针对生态系统中人为与自然干扰的诸多研究，均旨在检测生态变量或群落组成的差异。研究中常采用主成分分析（principal components analysis, PCA）、典范对应分析（canonical correspondence analysis, CCA）等排序分析方法，将复杂数据集简化为一组可表征原始变量间变异的核心因子。随后通过前两个主成分的散点图，可直观检视不同处理组间的群落组成差异。本文提出一种基于距离分析（analysis of distance, ANODIS）的方差分析多维扩展方法，该方法可利用原始样本观测的主成分分析或典范对应分析的1、2或更多维度，对群落组成差异开展正式统计检验。其显著性统计检验基于适配此类多维数据分析的F统计量。由于本分析属于参数检验方法，因此可便捷计算野外研究设计所需的检验功效与样本量。本文借助三项已发表研究中的双变量主成分分析散点图，演示了ANODIS的具体应用；同时通过非中心F分布，展示了统计检验功效的计算过程。