Experimental Design and Data Analysis for Biologists

In Chapter 9, we described multifactor ANOVA models that can involve crossed or nested factors, or a combination of both, and in Chapter 10, we introduced designs that incorporate either blocks or repeated measures. One particular class of experimental designs with both crossed and nested factors, and either blocks or repeated measures, includes split-plot designs (from an agricultural origin), and repeated measures designs (from psychology). These designs can be complex but are particularly common in biological research, so we have devoted a chapter to their analysis. We will use the term partly nested or partly hierarchical for the linear model we fit with these designs, and the least ambiguous name for these designs might also be partly nested. One of the important messages from this chapter is that these repeated measures and split-plot designs are basically analyzed with the same linear model, something that is often unappreciated by biologists, although some textbooks do emphasize the equivalence in models (e.g. Kirk 1995, Mead 1988). In its simplest form, this design has three factors: A and C are crossed, and B is nested within A but crossed with C, although the possible extensions of this design are almost limitless.

Partly nested designs

Split-plot designs

Split-plot designs were originally used in agricultural experiments and represent a randomized complete block (RCB) design, with one or more factors applied to experimental units within each block. A second factor (or set of factors) is then applied to whole blocks, with replicate blocks for each level of this factor.