Let equation be the observation at the , , and levels of A, B, and C respectively, where s = 0, 1,..., L 1. Express each observation as the sum of eight components. Thus,
where
is the overall mean.
is the average effect of the level of factor A.
is the average effect of the level of factor B.
is the average effect of the level of factor C.
is the two-factor interaction of the level of factor A with the level of factor B.
is the two-factor interaction of the level of factor A with the rth level of factor C.
is the two-factor interaction of the level of factor B with the rth level of factor C.
is the three-factor interaction of the level of factor A, the level of factor B, and the level of factor C.