Biostatistics with R An Introductory Guide for Field Biologists

The analysis of variance is introduced as a method of testing differences among means of more than two groups of observations. We outline the basic assumptions of ANOVA models, focusing on the expected homogeneity of variances across the compared groups, which is assessed by the Bartlett test. The decomposition of variability in the response variable (its total sum of squares) into among-group and within-group (residual) variation leads to the definition of the F-ratio, which is the central test statistic in ANOVA models. We also introduce the distinction between fixed and random effects and discuss the F test power as well as the robustness of the test to violations of ANOVA model assumptions. The first part of the chapter, dealing with one-way ANOVA, concludes with a description of the multiple comparisons procedure. We focus on two types - Tukey's test and Dunnett's test. This chapter concludes by presenting a nonparametric counterpart of one-way ANOVA, the Kruskal-Wallis test. The methods described in this chapter are accompanied by a carefully-explained guide to the R code needed for their use, including the multcomp package.