A carefully planned investigation can give much more insight into the question at hand than a haphazard one, data from which may be useless. Experimental design is a highly developed subject, though its principles are not universally appreciated. In this chapter we outline some basic ideas and describe some simple designs and associated analyses. The first section discusses the importance of randomization, and shows how it can be used to justify standard linear models and how it strengthens inferences. Section 9.2 then describes some common designs and analyses. Interaction, contrasts and analysis of covariance are discussed in Section 9.3. Section 9.4 then outlines the consequences of having more than one level of variability.

Randomization

Randomization

The purpose of a designed experiment is to compare how treatments affect a response, by applying them to experimental units, on each of which the response is to be measured. The units are the raw material of the investigation; formally a unit is the smallest subdivision of this such that any two different units might receive different treatments. The treatments are clearly defined procedures one of which is to be applied to each experimental unit. In an agricultural field trial the treatments might be different amounts of nitrogen and potash, while a unit is a plot of land. In a medical setting, treatments might be types of operation and different therapies, with units being patients who are operated upon and then given therapy to aid recovery.