It’s surprisingly common for biologists to combine crossed and nested factors. These designs are partly nested or split-plot designs. They are nearly always mixed models, usually a random nested effect and at least two fixed effects. We describe the analysis of these designs, starting with a simple three-factor design with a single between-plot and a single within-plot effect, extending this analysis to include multiple effects, including interactions at this level, and adding continuous predictors (covariates).

This chapter handles more advanced types of ANOVA models, those that contain multiple explanatory variables (factors). We start with the hierarchical ANOVA, illustrated by two example studies, and we describe how the variation of the response variable is decomposed, introducing the concept of variance components. We set apart and discuss the properties of the split-plot ANOVA model and we illustrate its use by evaluating the results of a field experiment. Finally, we discuss the repeated measurements ANOVA, which is a very important model for analysing both monitoring data and data from manipulative experiments. Although it is typically analysed using a type of a split-plot ANOVA, the repeated measurements ANOVA model has further assumptions that are discussed in the text. The methods described in this chapter are accompanied by a carefully-explained guide to the R code needed for their use, including the nlme, lme4, effects, and car packages.