3D ANOVA Statistical Model

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.
• is random fluctuation.