In a one-way ANOVA, the sum of squares can be obtained in a straightforward manner. However, in a two-way ANOVA, things get much more complicated because we have at least three possibilities for computing them. For the following examples, let's assume that we have two factors (A and B), each one with their respective levels.
Type I, Type II, and Type III sum of squares
Type I
The first possibility is the Type I sum of squares, which can be computed by first calculating the sum of squares for factor A, then the sum of squares of B conditional on A, and finally the sum of squares of the interaction (AB) after including the factors, A and B. This is why this is called the sequential sum of squares. Consequently, the order...