Biostatistics with R An Introductory Guide for Field Biologists

The two-way ANOVA , is applied to data with a factorial arrangement (and its extensions to more factors), and is an important tool for analysing data from experimental studies. We start by characterising the properties of a factorial design and compare it with a hierarchical design. We introduce two important experimental concepts here - the ideas of a balanced design and of a proportional design. We then describe the two-way ANOVA model, including an explanation of the interaction term and its use in ANOVA models. We outline some basic types of correct experimental designs, including complete randomised blocks, and contrast them with incorrect designs resulting in pseudo-replicated observations. Separate sections deal with ANOVA model specification for randomised blocks and Latin square designs, and with the specific issues of the multiple comparisons procedure in ANOVA models with multiple factors. A nonparametric counterpart of the randomised complete block ANOVA - the Friedman test - is also introduced. 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.