Consider a two way layout in which the effects of the factors are additive so that Eq (11 7 1) is satisfied, and let v 1 , , v I and w 1 , , w J be arbitrary given positive numbers Show that there exist unique numbers , 1 , , I , and 1 , , J such that and E(Y ij ) I J for i 1, , I and j 1, , J 0 j 1 i 1

Question: Consider a two-way layout in which the effects of the factors are additive so that Eq. (11.7.1) is satisfied, and let v 1 , .

Consider a two-way layout in which the effects of the factors are additive so that Eq. (11.7.1) is satisfied, and let v₁, . . . , v_I and w₁, . . . , w_J be arbitrary given positive numbers. Show that there exist unique numbers μ, α₁, . . . , α_I , and β₁, . . . , β_J such that

and

E(Y_ij) = μ + α_I+ β_J for i = 1, . . . , I and j = 1, . . . , J.

- -0 j=1 i=1

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