5.8. Full factorial designs

In this section we learn how, and why, we should change more than one variable at a time. We will use factorial designs because

  • We can visually interpret these designs, and see where to run future experiments;

  • These designs require relatively few experiments; and

  • They are often building blocks for more complex designs.

Most often we have two or more factors that affect our response variable, \(y\). In this section we consider the case when these factors are at two levels. Some examples would be to operate at low or high pH, select long operating times or short operating times, use catalyst A or B and use mixing system A or B. The general guidance is to choose the low and high values at the edges of normal operation. It is not wise to use the minimum and maximum values that each factor could possibly have; they will likely be too extreme. We will see an example of this in the section on saturated designs.