Now we are ready to calculate the interaction between Factors AxB. This is a very simple calculation that is obtained by taking the sums of squares for between groups (which was calculated from the squared deviations of each cell total from the grand mean estimate) and removing the main effects estimates. We can think of each cell as consisting of three factors -- main effects for A, main effects for B, and the interaction between A and B. If we want to know only about the interaction, then we must remove the main effects from our estimates.

Formula

In this calculation, we use the estimates that we obtained in previous calculations. This might be a good time to check and make sure that those calculations are accurate.

As we can see, the sums of squares for the interaction between A x B has a very small value. It is highly unlikely that the interaction between these two factors is statistically significant.