midterm08

# midterm08 - c = 1-1-1 1(a Using the quadratic model E Y | X...

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Midterm 1. Consider the following 2 3 replicated (n=2) factorial design: Run Response (1) 121.6, 121.4 a 129.3, 127.3 b 104.8, 107.4 ab 144.7, 143.5 c 126.7, 123.4 ac 129.4, 126.0 bc 111.1, 108.2 abc 142.5, 146.4 (a) Compute the MSPE for this experiment; you will use it as an estimate of σ for sample size calculations. Assume α = . 05 for the following questions. (b) Suppose we wished to detect an A main eﬀect of size -2 with 80% power. How large a sample size would we need? (c) Suppose we wished to detect an AB interaction eﬀect of size 1.5 with 90% power. How large a sample size would we need? (d) Researchers sometimes like to compute posterior, or observed, power. Estimate the A and B main eﬀects from the above experiment, and then use these estimates to compute the observed power for detecting A and B eﬀects of these magnitudes. 2. Consider a CRD on the quantitative factor X with levels 24, 28, 32, and 36. We are interested in the quadratic contrast L Q = c 1 E ( Y | X = 24)+ ... + c 4 E ( Y | X = 36) with contrast coeﬃcients

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Unformatted text preview: c = ( 1 ,-1 ,-1 , 1 ). (a) Using the quadratic model E ( Y | X ) = β + β 1 X + β 2 X 2 , write L Q as a function of β 2 . Argue that a test of L Q = 0 is equivalent to a test of β 2 = 0. (b) Can you make the same argument about L Q for the cubic model E ( Y | X ) = β + β 1 X + β 2 X 2 + β 3 X 3 ? What conclusions can you reach about the test for a quadratic eﬀect? 1 3. Suppose we have a 3 by 3 table with the following set of observed sample responses. B 12,3 17 A 10,11 3 19, 16, 17 (a) For the additive model, are the population marginal means for A and B estimable? (b) Add the observations 6 and 12 to the (2,3) cell. Are the population marginal means for A and B estimable? Brieﬂy explain any diﬀerences between your two results. (c) Using the augmented data set, compare and contrast the Type III and Type IV hypotheses for the interaction model for A, B and AB. 2...
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midterm08 - c = 1-1-1 1(a Using the quadratic model E Y | X...

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