In a two-way 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.

This is a fundamental principle of ANOVA and is true for all types of ANOVA. The total sum of squares represents the variability in the dependent variable that can be attributed to all sources of variation, including the main effects of each factor, the interaction between the factors, and the residual or error variance. The sum of squares due to the main effects and the interaction must add up to the total sum of squares because they represent all possible sources of variability that might explain the variability in the dependent variable. The error sum of squares is a measure of the variability in the dependent variable that cannot be explained by the main effects or the interaction between factors.