It is now time to calculate our final sums of squares. This term serves as our estimate of error in our hypothesis tests. We can calculate this value directly or we can obtain it by subtracting the sums of squares for the between-groups effects from the total sums of squares. The subtraction method is easiest and is most commonly used.

Formula

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

Now that we have obtained all of our necessary sums of squares, we are ready to proceed with testing our hypotheses about the factors in our design.