Consider a two-way cross-classified model given by Where δ ij = γ ij − .j and {α i }, {β j }, {γ k }, and {ϵ ij k} are as defined in Exercise 18.5. That is, here we are assuming that the interaction...

Consider a two-way cross-classified model given by

Where δ_ij
= γ_ij
−
.j and {α_i}, {β_j}, {γ_k}, and {ϵ_ijk} are as defined in Exercise 18.5. That is, here we are assuming that the interaction effects sum to zero
over the index for the fixed effects. Do Parts (a) through (d) in Exercise 18.5.

Exercise 18.5

Consider a two-way cross-classified model given by

(a) Give the ANOVA table and compute the expected mean squares.

(b) Use the expected mean squares to derive the unbiased estimators of the variance components.

(c) Derive the standard errors of the unbiased estimators in (b).

(d) Give the test statistics for testing H₀: α₁
= ··· = α_a
and H₀: σ²
_β
= 0.