Balanced and unbalanced designs

If your design is balanced, meaning that the relative frequency distribution of the independent variables is approximately equal, the experimental factors are considered statistically independent, and therefore three effects (main effects plus interaction) can all be estimated and evaluated independently.

When the relative frequencies of factor A differ across levels of factor B, the design is non-orthogonal → the factors are statistically associated and effects of interest, main effects, and interaction effect cannot be tested independently.

Typically, one corrects for this by disentangling the various effects of interest with Type III Sum of Squares.

However, when dealing with an unbalanced (non-orthogonal) design, the main effects cannot be interpreted in a model that includes an interaction term.