The R Book, 3rd Edition

16Designed Experiments

There are a number of analyses using that commonly arise when we design our own study or experiment and those that are not covered in the other modelling chapters are included here. They can be used for observational studies, etc., but, typically, they work most effectively where we have control over the process that is being analysed. A good introduction to and discussion of the design and analysis of experiments can be found in Cox and Reid, 2000. In this chapter, we will assume that we have the data and want to draw every last ounce/gram/grain of information from them.

16.1 Factorial experiments

A factorial experiment is a designed experiment where all the covariates are categorical, usually each having a small number of levels, and the outcome is usually continuous. The experiment is usually carried out for each combination of factor levels. If each combination is repeated, then we have replicates. For instance, we might be interested in the volume of a loaf of bread where we have low and high levels of both yeast and flour together with a proving time, where the mixture rests and expands, of 20 and 40 minutes. Although the final explanatory variable is numerical, it takes only two values and so we shall consider it as categorical. There are eight combinations of the three factors and as each has two levels this is known as a experiment. There are ...