In a three-way layout with one observation in each cell,
Chapter 11, Problem 23(choose chapter or problem)
In a three-way layout with one observation in each cell, the observations Yijk (i = 1,...,I ; j = 1,...,J ; k = 1,...,K) are assumed to be independent and normally distributed, with a common variance 2. Suppose that E(Yijk) = ijk. Show that for every set of numbers ijk, there exists a unique set of numbers , A i , B j , C k , AB ij , AC ik , BC jk , and ijk (i = 1,...,I ; j = 1,...,J ; k = 1,...,K) such that A + = B + = C + = 0, AB i+ = AB +j = AC i+ = AC +k = BC j+ = BC +k = 0, ij+ = i+k = +jk = 0, and ijk = + A i + B j + C k + AB ij + AC ik + BC jk + ijk, for all values of i, j , and k
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