DoE Lecture 3: Cochran's Theorem

We discuss the question, why do we do F-tests when analysing ANOVA models? The rest of this lecture is dedicated to proving Cochran's theorem, the main mathematical tool for design of experiments.

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15:30 For anyone wondering why z'z = sum of Qk implies that A1 + A2 + ... = identity, the reason is as follows. Let z'z = sum of Qk = sum of z'Akz = z'A1z + z'A2z + ... = z'(A1z + A2z + ...) = z'(A1 + A2 + ...)z;

Thus, the statement is essentially this: let z'z = z'(A1 + A2 + ...)z. Therefore, the sum of A1 + A2 + ... + An = identity