In a two-factor ANOVA, the sum of squares due to both factors, the interaction sum of squares, and the error sum of squares, must add up to the total sum of squares.

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This is true because the total variability in the response variable can be decomposed into three sources: the variability attributable to the main effects of the two factors, the variability due to their interaction and the variability that cannot be accounted for by these two sources (i.e., error variability). Therefore, the sum of squares due to both factors, the interaction sum of squares, and the error sum of squares must add up to the total sum of squares.

In a Two-Factor ANOVA, the Sum of Squares Due to Both