# Final08 - and 2006. The assignment of plots to treatments...

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Final Exam 1. Return to the Wheat data set we studied in Problem 22.5 for Homework 5. (a) For the ﬁxed eﬀects model (i.e., both ploidy and species(ploidy) are ﬁxed), compute both MEANs and LSMEANs. Compare them. (b) Verify empirically that the LSMEANs for ploidy is an estimate of PMM ( α i ) = b i X j =1 μ ij = μ + α i + ¯ β . ( i ) , i = 1 ,...,a by comparing the average of the species(ploidy) means for each level of ploidy to LSMEANs for ploidy . (c) Derive an expression for the expected value of the ploidy means (it should have a form similar to the expression for PMM ( α i ) that I provided above). Compare these two population means. Which do you prefer as a summary measure of the ploidy population mean? Do you see shortcomings with your preferred approach? 2. A researcher studying plant biomass selected 16 plots. Each plot was assigned to one of four treatment combinations: a cross-classifcation of Controlled Burn/No Burn and Irrigation/No Irrigation. Total understory biomass was measured in 2003, 2004, 2005
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Unformatted text preview: and 2006. The assignment of plots to treatments appears below: Plot Burn Irrigate 1 No No 2 No Yes 3 Yes No 4 No No 5 Yes No 6 No Yes 7 Yes No 8 No Yes 9 Yes Yes 10 Yes Yes 11 Yes No 12 Yes Yes 13 Yes Yes 14 No No 15 No No 16 No Yes (a) Identify the design. (b) Using the data from the website, analyze the design. Be sure to specify a response and justify your nal model. Include graphs and diagnostics. Ignore the variable Overstory for now. 3. Return to the above experiment. The researchers had noted that the plots had varying amounts of large trees (overstory) that could aect the growth of understory, and so had grouped the plots into 4 separate overstory categories. Using the Overstory variable, reanalyze the data, noting any problems the addition of Overstory creates. 1...
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