Experimental Design and Data Analysis for Biologists

In Chapter 8, we examined designs with a single factor where the appropriate linear model had a single categorical predictor variable. Commonly in biology, however, we design studies with more than one factor and there are two main reasons why we might include additional factors. First, to try and reduce the unexplained (or residual) variation in our response variable, similarly to multiple regression (Chapter 6). Second, to examine the interactions between factors, i.e. whether the effect of a particular factor on the response variable is dependent on another factor. In this chapter, we will examine two types of multifactor design, nested and factorial, and describe the appropriate linear models for their analysis. The emphasis is on completely randomized (CR) designs, following from Chapter 8, where the experimental units are randomly allocated to factor groups or combinations of factor groups.

Nested (hierarchical) designs

A common extension of the single factor design, and the single factor ANOVA linear model, is when additional factors are included that are nested within the main factor of interest. An example based on a manipulative experiment comes from Quinn & Keough (1993) who examined the effect of different enclosure (fence) sizes on growth of the rocky intertidal limpet Cellana tramoserica. Part of that experiment used two enclosure sizes (1225 cm2 and 4900 cm2), with five replicate enclosures nested within each size and four or five replicate limpets from each enclosure. The response variable was limpet shell height.