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homework.1

# homework.1 - cell means null hypothesis If our alternative...

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Homework 1 1. For the following data, use orthogonal polynomial contrasts to test whether or not a linear model is better than an intercept model; whether or not a quadratic model (with a linear term) is better than an intercept model. Are either of these models inferior to the usual cell means model? X 5 10 15 20 3.8 36.2 41.0 42.8 7.1 22.6 34.0 57.9 14.6 24.2 34.2 43.6 14.5 13.9 29.6 58.8 2. Consider only the 4 tree soils from the Soil data (refer to problems 5.3 and 5.4). (a) Plot the response (pathogen score) as a function of the 4-level factor. (b) Test for factor-level differences. (c) Analyze the residuals. (d) Use a contrast to compare the mean response for nm-6 to the mean response averaged over the other three tree soils. (e) Find two other mutually orthogonal contrasts to the contrast above. Confirm that the contrast sum of squares sum to the treatment sum of squares. 3. Suppose we want to have 90% power to detect an alternative hypothesis to the equal
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Unformatted text preview: cell means null hypothesis. If our alternative hypothesis is H a : μ 1 = μ 3 = μ 4 = 60; μ 2 = μ 5 = 70, and σ 2 = 30, what sample size would we need to achieve our target power? Repeat the calculation for σ 2 = 40, 50, and 60. Comment. 4. Assume that the density of ﬁddler crab burrows is being tested for four diﬀerent types of habitat using a CRD. The research wants to conduct a power analysis on the contrast between the mean number of burrows in the ﬁrst habitat against the average of the mean number of burrows in the remaining three habitats. Suppose that the number of burrows has a variance of 20 and the researcher is testing H o : μ 1-μ 2 + μ 3 + μ 4 3 = 0 using a α = . 05 test. Summarize the size of the contrasts that the researcher will be able to detect with 80% power. 1...
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• Spring '08
• JohnM.Grego
• Null hypothesis, researcher, orthogonal polynomial contrasts, mutually orthogonal contrasts, tree soils

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