The formulas for sums of squares given in the section on partitioning the variance are not the most efficient computationally. They were chosen because they help to convey the conceptual basis of analysis of variance. This section provides computational formulas. Most likely you will not often have to use these formulas since analysis of variance is usually done by computer. Nonetheless, if you ever need to do an ANOVA with a hand calculator, these formulas may help. Data from a hypothetical experiment on pain relief described earlier are reproduced below.

Aspirin Tylenol Placebo 3 2 2 5 2 1 3 4 3 5 4 2The sum of squares total (SST) can be calculated as:

where

and N is the total number of subjects.

For these data: CF = (3+5+3+5+2+2+4+4+ 2+1+3+2)²/12 = 36²/12 = 108.