Question: In a fixed-effects model, suppose that there are n observations for each of four treatments. Let Q 2 1 Q 2 2 , and Q

In a fixed-effects model, suppose that there are n observations for each of four treatments. Let Q²₁ Q²₂, and Q²₃be single-degree-of-freedom sums of squares for orthogonal contrasts. A contrast is a linear combination of the treatment means with coefficients that sum to zero. The coefficient vectors of orthogonal contrasts are orthogonal vectors. Prove that SS_Treatments = Q²₁ +Q²₂ + Q²₃.

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