Polynomial Contrasts

Abstract

The experiments we have considered so far have always involved treatments which arequalitativein nature: for example, variety of lupin or breed of sheep. Consequently the contrasts of interest were comparisons of one class of treatment with another (Chapter 8). In the case of factorial experiments (Chapter 9) the contrasts of interest also included the interactions between factors. Frequently in an experimental situation, however, the treatments arequantitativein nature. Such is the case when treatments correspond to the seeding rate of barley in kg/ha, or the dose rate of a medicine in a clinical trial in mg/person. In the first example, it is then natural to ask a question of the type “Does the yield of barley increase as the seeding rate increases?” In the second example, the natural question may be “Does blood pressure go down as dose rate goes up?” In this chapter we find out how to answer such questions. The mechanism will be essentially that of the previous two chapters: the effects we wish to study correspond to contrasts, and testing is carried out using the appropriate unit vector in the treatment space.