Partitioning the Sums of Squares (3 of 7)
Total Sum of Squares
The variation among all the subjects in an experiment is measured by what is called sum of squares total or SST. SST is the sum of the squared differences of each score from the mean of all the scores. Letting GM (standing for "grand mean") represent the mean of all scores, then
SST = Σ(X - GM)²
where GM = ΣX/N and N is the total number of subjects in the experiment
For the example data:
N = 12
GM = (3+5+3+5+2+2+4+4+2+1+3+2)/12 = 3
SST = (3-3)²+(5-3)²+(3-3)²+(5-3)² + (2-3)²+(2-3)²+(4-3)²+(4-3)² + (2-3)²+(1-3)²+(3-3)²+(2-3)² = 18
Sum of Squares Between Groups
The sum of squares due to differences between groups (SSB) is computed according to the following formula:
where ni is the sample size of the ith group and Mi is the mean of the ith group, and GM is the mean of all scores in all groups.