Partitioning the Sums of Squares (4 of 7)
If the sample sizes are equal then the formula can be simplified somewhat:
SSB = nΣ(Mi - GM)²
For the example data,
M1 = (3+5+3+5)/4 = 4
M2 = (2+4+2+4)/4 = 3
M3 = (2+1+3+2)/4 = 2
GM = 3
n = 4
SSB = 4[(4-3)² + (3-3)² + (2-3)²] = 8
Sum of Squares Error
The sum of squares error is the sum of the squared differences between the individual scores and their group means. The formula for sum of squares error (SSE) for designs with two groups has already been given in the section on confidence interval on the difference between two independent means and in testing differences between two independent means.
The SSE is computed separately for each of the groups in the experiment and then summed.
SSE = SSE1 + SSE2 + ... + SSEa
SSE1 = Σ(X - M1)² ; SSE2 = Σ(X - M2)² SSEa = Σ(X - Ma)² where M1 is the mean of Group 1, M2 is the mean of Group 2, and Ma is the mean of Group a.