By R. A. Bailey

ISBN-10: 0511393407

ISBN-13: 9780511393402

ISBN-10: 0521683572

ISBN-13: 9780521683579

ISBN-10: 0521865069

ISBN-13: 9780521865067

The coherent framework in the back of stable perform; for operating statisticians, complicated undergraduates, starting graduate students.

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**Extra resources for Design of Comparative Experiments**

**Example text**

1 so put r = 5. Then d = 8. 04. Thus we put r = 4. Then d = 6. 4. 6), so we stop. We conclude that eight experimental units should suffice. Note that power can be increased by including extra treatments (because this increases d) but that this does not alter the variance of the estimator of a difference between two treatments. 5. As before, we assume that E (Y) = τ ∈ VT . However, we change the assumption about covariance to cov(Zα , Zβ ) = σ2 ρσ2 if α = β if α = β. In other words, the correlation between responses on pairs of different plots is ρ, which may not be zero.

8, with R = N − r1 , shows that this average variance is minimized when r2 = r3 = · · · = rt = (N − r1 )/(t − 1). Put r1 = r and 1 t t −1 1 t −1 1 = + , g(r) = + ∑ r t − 1 i=2 N − r r N −r so that we need to choose r to minimize g(r). Now, g is differentiable on (0, N) and increases without limit as r → 0 and as r → N. Moreover, 1 (t − 1) + , r2 (N − r)2 √ which is zero when, and only when, r = (N − r)/ t − 1. Thus g(r) is minimized when, and √ only when, r = (N − r)/ t − 1; that is √ √ r1 = r = (t − 1)r2 / t − 1 = t − 1 r2 .

I Hence EMS(treatments) = ∑i ri τ2i − N τ2 + σ2 . 3513. 8964. 9482. 12. 12 33 Hypothesis testing The previous section shows how to decompose the vector space V into the sum of three orthogonal pieces: V = VT ⊕VT⊥ = V0 ⊕WT ⊕VT⊥ . Correspondingly, the overall dimension N, the data vector y and its sum of squares can all be shown as the sum of three pieces. The sums of squares have their corresponding mean squares and expected mean squares, although there is no longer any sense in adding the three pieces.

### Design of Comparative Experiments by R. A. Bailey

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