For an I J table, let ij = log ij , and let a dot subscript denote the mean for that index

For an I × J table, let η_ij = log µ_ij, and let a dot subscript denote the mean for that index (e.g., η_i. = ∑_j η_ij/J). Then, let λ = η.., λ_i^X = η_i.– η.., λ_j^Y = η._j – η.., and λ_ij^XY = η_ij – η_i. – η._j + η..·

a. For 2 × 2 tables, show that log θ = 4λ₁₁^XY.

b. For 2 × J tables, show that λ₁₁^XY = (∑_j log α_j)/2J, where α_j = µ₁₁ µ_2j/µ₂₁ µ_1j, j = 2,..., J.