Experimental Design and Data Analysis for Biologists

Predictors can be fixed or random, and their classification affects how we fit and interpret statistical models. A mismatch between their treatment in the model and their interpretation is a common problem. This chapter focuses on categorical predictors and introduces nested or hierarchical designs that combine fixed and random effects. For these designs, we distinguish between those where the random effects correspond to replicate experimental and sampling units and those that also include multiple observational units within each replicate. We also consider factorial mixed models and introduce hybrid designs that combine factorial and nested components. We describe the fitting of these models using traditional “ANOVA” approaches using OLS and present an alternative approach used in the following chapters – linear mixed models or multilevel models. These modeling approaches are illustrated for multilevel nested designs and factorial designs with and without replication.