Table 9.

Demonstration of the differing approaches to producing marginal means in the presence of interaction effects using either equally weighted or frequency weighted cell means.

Approach	Cell 1	Cell 2	Result
Averaged – ignoring cells	7	8,9	8
Equally weighted means (Type III)	$\frac{1}{2}\times 7$	$\frac{1}{2}\times 8.5$	7.75
Frequency weighted means (Type I–II)	$\frac{1}{3}\times 7$	$\frac{2}{3}\times 8.5$	8