Calculating Sum - of - Squares A ( SSA )

In previous chapters we analyzed data from so-called one-way experimental designs, in which subjects were randomly assigned to groups that di↵ered on a single treatment or grouping variable. In this chapter we will analyze data from factorial experiments. Factorial experiments contain two or more experimental variables. In a completely crossed factorial experiment, each level of every variable is combined with each level of every other variable. So, if there are two variables with a and b levels, then there will be ab combinations of treatments, which are sometimes called cells. Subjects are then assigned randomly to the various combinations of treatments. Experiments that have equal n per cell are called balanced designs. Designs with unequal n are unbalanced. We will start by analyzing data from balanced designs, and then consider unbalanced data near the end of this chapter. Our analyses will focus on factorial experiments with two experimental factors, A and B. (Higherorder factorial designs are examined in chapter 8.) The design of a factorial experiment that has two variables can be represented as a two-dimensional table, with the rows representing di↵erent levels of variable A and the columns representing di↵erent levels of variable B. Each cell within the table corresponds to a particular combination of treatments. For example, a