Formal Model (1 of 2)
In an analysis of variance design, each score in the "a"
populations can be defined in terms of the following formal
model:
y
_{ij} = μ
_{g} + α
_{j} + ε
_{ij}
where:

y_{ij} is the score of the ith subject in the
jth population,
 μ_{g} is the mean of all the population means,
 α_{j} equals μ_{j}  μ_{g} where μ_{j} is
the mean of the jth population,
 α_{j} represents the effect of being in the jth population,
where
Σα_{j} = 0,
 ε_{ij} is the
sum of all other effects on the ith person in the jth population and
is referred to as error.
The error within
each population is assumed to be
normally distributed
and have a mean of zero. The error variances within the "a" populations
are assumed to be equal.