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midterm.05

midterm.05 - Midterm 1 Consider a RCBD comparing a control...

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Midterm 1. Consider a RCBD comparing a control to new treatments A, B, C, and D. Under the usual ANOVA null hypothesis H o : μ 1 = . . . = μ a , suppose the experimenter wants to be able to detect when each treatment mean is k units greater than the control mean at α = . 01. (a) Find the noncentrality parameter λ for the researcher’s alternative as a function of k . (b) Conduct an analysis of the pilot study below. (c) Write a SAS program to compute power for various choices of k and b . Use an estimate of σ from the pilot study. Construct a contour plot with k and b as the coordinate axes. (d) How many blocks would we need to detect k = . 1, k = . 2, k = . 3 with 80% power? Block Treatment 1 2 3 Control 9.60 9.61 9.52 A 9.75 9.64 9.79 B 9.87 9.83 9.60 C 9.72 9.82 9.69 D 9.56 9.90 9.87 2. Consider the following SAS output from analysis of a two-way model. (a) Compute variance components assuming both factors are random. (b) Construct tests for A, B and AB for both the unrestricted and restricted mixed effects models. Assume A is fixed and B is random for this exercise. Source DF Type III SS Mean Square F Value Pr>F A 2 5467.85 2733.93 30.03 .000 B 4 2451.90 612.97 6.73 .003 A*B 8 1857.29 232.16

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midterm.05 - Midterm 1 Consider a RCBD comparing a control...

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