Experimental Design and Data Analysis for Biologists

In Chapter 9, we described the analyses of completely randomized (CR) designs where the factors were either crossed with, or nested in, others. There are several other experimental designs that have special analytical requirements, and are used very commonly in the biological sciences. These include unreplicated factorial designs and designs that combine crossed (factorial) and nested arrangements. We deal with these two groups of designs in the next two chapters. In most cases, the main aim of these designs is to reduce the unexplained variation (MSResidual) compared to a CR design. Such designs can be more efficient than CR designs, i.e., they offer more precise estimates of parameters and more powerful tests of the null hypotheses of interest, with no increase in the overall resources needed for the experiment. In contrast to CR designs, however, they involve restricted randomization of factor levels to experimental units and usually have additional assumptions. We will consider the simplest of these designs in this chapter.

We also recommend that biologists distinguish between the physical design (or structure) of an experiment and the linear model used to analyze it. The same model can be applied to a number of different experimental designs and we find some of the literature on these analyses confusing because the label used for the design is often interchanged with the label used for the analysis.

Unreplicated two factor experimental designs

A class of experimental designs commonly used in biology is based on a two factor crossed (factorial) design with a single observation in each cell.