By Dogeu D. (ed.), Lucaks E. (ed.), Rohatgi V.K. (ed.)

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RNA samples were labeled and divided into two identical aliquots for independent hybridizations, denoted A and B. Thus, data for 6,800 genes on the microarray were generated from 8 hybridizations (U1A, U1B, U2A, U2B, I1A, I1B, I2A, and I2B) according to the treatment design. The analysis done by Tusher et al. (2001) interpreted the design for one gene as Treatment I U x x x x x x x x Anova Source Treatments(U/I) Within Total df 1 6 7 24 1 Basics which treats the design as a two-sample t-test (a oneway CRD).

Note: Perhaps the easiest way to understand the distinction between orthogonal and uncorrelated is realize that we should only use orthogonal (or nonorthogonal) for contrasts in parameters, and we should only use correlated (or uncorrelated) for contrasts in statistics. 4). 12, two contrasts i=1 i i i=1 i i o a b = 0. The same two orthogonal if their deﬁning vectors are at 90 , so i i i contrasts are uncorrelated if Cov( i ai Yi , i bi Yi ) = 0. 15) Cov i bi Y¯i ai bi Var(Y¯i ) + 2 = i i ai bi Cov(Y¯i , Y¯i ), i>i a b Var(Y¯i ) = 0.

R and εijk ∼ N(0, σ 2 ), independent. Show that SS(A)/σ 2 and SS(B)/σ 2 are independent χ2 random variables, and verify their degrees of freedom. 8 Technical Notes 37 (c) Show that SS(Within)/σ 2 is also χ2 , independent of the Sums of squares in part (b), and hence establish the validity of the usual F -test on main eﬀects. Note also that SS(A × B)/σ 2 , where SS(A × B) is the interaction sum of squares, is also χ2 , independent of everything else. 26. 1 Estimability Although it is typical, especially in design books, to talk about estimability in terms of unbiasedness, as we have done, this is quite a limiting view.

### Analytical Methods in Probability Theory: Proceedings by Dogeu D. (ed.), Lucaks E. (ed.), Rohatgi V.K. (ed.)

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