2D ANOVA Statistical Model
Let
be the
observation at the
and
levels of A and B respectively, where r = 0,1,...,L 1.
Model 1 expresses each observation as the sum of four components.


Models 2, 3, and 4 express each observation as the sum of five components.

where

is the overall mean response (the average of the mean response for all the populations).
is the effect of the
level of factor A
(equal to
where
is the average of the
level of factor A over all levels of factor B).
is the effect of the
level of factor B
(equal to
where
is the average of the
level of factor B over all levels of factor A).
is the interaction between the
level of factor A and the
level of factor B
(equal to
where
is the population mean of the
cell).
is the deviation of
from the population mean response for the
population.