Table : TABLE 14-17. Calculating the Within-Groups Sum of Squares The within-groups sum of squares is calculated the same way for a two-way ANOVA as for a one-way ANOVA. We take each score and subtract the mean of the cell from which it comes—not the grand mean—to create deviations; then we square the deviations and sum them: Σ(X − Mcell)2 = 0.018.
X∑(X − Mcell)∑(X − Mcell)2
   Y, 1   0.25   (0.25 − 0.20) = 0.05   0.0025
   0.21   (0.21 − 0.20) = 0.01   0.0001
   0.14   (0.14 − 0.20) = 20.06   0.0036
   Y, 3   0.07   (0.07 − 0.12) = 20.05   0.0025
   0.13   (0.13 − 0.12) = 0.01   0.0001
   0.16   (0.16 − 0.12) = 0.04   0.0016
   O, 1   0.27   (0.27 − 0.22) = 0.05   0.0025
   0.22   (0.22 − 0.22) = 0.00   0.0000
   0.17   (0.17 − 0.22) = 20.05   0.0025
   O, 3   0.33   (0.33 − 0.30) = 0.03   0.0009
   0.31   (0.31 − 0.30) = 0.01   0.0001
   0.26   (0.26 − 0.30) = 20.04   0.0016