2D ANOVA General Method

In each of the models, the VI breaks up the total sum of squares, tss, a measure of the total variation of the data from the overall population mean, into some number of component sums of squares. In model 1

tss = ssa + ssb + sse

whereas in models 2 through 4

tss = ssa + ssb + ssab + sse

Each component sum in tss is a measure of variation attributed to a certain factor or interaction among the factors. Here ssa is a measure of the variation due to factor A, ssb is a measure of the variation due to factor B, ssab is a measure of the variation due to the interaction between factors A and B, and sse is a measure of the variation due to random fluctuation. Notice that with model 1 you have no ssab term. This is what no interaction means.

The VI divides each of the values ssa, ssb, ssab, and sse by their own degrees of freedom to compute the mean square quantities msa, msb, msab, and mse. If one factor, such as factor A, has a strong effect on the experimental observations, the respective mean square quantity msa will be relatively large.