TABLE OF CONTENTS Just as 2 f factorial experiments represent an interesting special case of factorial experimentation, so also do 3 f factorial experiments. The 3 f factorials consider f factors at three levels; thus there are 2 degrees of freedom between the levels of each of these factors. The 3 f factorials play an important role in more complicated design problems, which are discussed in subsequent chapters. For this chapter, we assume that the design is a completely randomized design and that the levels of the factors considered are fixed levels. Such levels may be either qualitative or quantitative.
For a three-level factor, one can partition the 2 degrees of freedom into two orthogonal constrasts, each with 1 degree of freedom, as shown in Chapter 3.
If an experiment can be designed such that the levels of an effect are quantitative and equispaced, two orthogonal contrasts can be found that will have physical meaning in terms of the equispaced variable, say X.
Figure 10.1 shows three equispaced levels of a factor X (namely, X 1, X 2, and X 3) and the corresponding responses of a Y variable at these three points. The Y totals are shown as T .1, T .2, and T .3. In Figure 10.1, if X increases from X 1 to X 3, the increase in response totals goes from T .1
