In previous chapters we have emphasized experiments with a single unstructured set of treatments. It is very often required to investigate the eect of several dierent sets of treatments, or more generally several dierent explanatory factors, on a response of interest. Examples include studying the eect of temperature, concentration, and pressure on the hardness of a manufactured product, or the eects of three dierent types of fertiliser, say nitrogen, potassium and potash, on the yield of a crop. The dierent aspects dening treatments are conventionally called factors, and there are typically a specied, usually small, number of levels for each factor. An individual treatment is a particular combination of levels of the factors.