In the two-fold nested model, with unequal but non-zero cell frequencies, the parameterization in (12.46) is often replaced by either of the following definitions of the parameters. Hip-Hab = - -- where

a, is defined for i=1, (a-1) and is defined for i 1, and J-1,(6-1).

a. Determine the parameter matrix for each choice of parameters.

b. Determine the hypotheses, expressed in terms of the cell means, associated with the sums of squares R(or p.7) and R

(a) for each choice of parameters.

e. Determine simple algebraic expressions for each of the numerator sums of squares in part b

d. Determine the hypothesis associated with the sum of squares R(a | ) in each case. Section 12.5