4b_ mixed mod_pt2 - Motivating texts Advanced Topics in...

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Advanced Topics in Forest Biometrics – FOR6934 Mixed Models – Part II Fal 2007, C. Staudhammer Slide 2 Motivating texts Schabenberger, O. and F.J. Pierce (2002) Contemporary Statistical Models for the Plant and Soil Sciences . CRC Press, NY, NY. Littell, R.C., G.A. Milliken, W.W. Stroup, and R.D. Wolfinger (1996) SAS System for Mixed Models . SAS Institute, Cary,NC. Fal 2007, C. Staudhammer Slide 3 Outline 1. What are repeated measures? 2. How are they different from the basic designs we covered? 3. Examples of repeated measures experiments Fal 2007, C. Staudhammer Slide 4 What are repeated measures? ± Repeated measures are observations taken on the same experimental unit, called a subject ² Subjects are dependent groups ² The same subjects are used for each treatment ± Repeated measure can be made over time (in sequence) or over space Fal 2007, C. Staudhammer Slide 5 Examples of repeated measures ± Diameter of a tree, measured annually for ten years ± Monthly weight of salmonids over the first year of life ± pH of river, measured weekly ± Thickness of primate vertebrae, going up the spine ± Diameter of a tree, measured at 1-meter increments along its stem ± pH of river, measured at 100-meter intervals from a pulp mill Fal 2007, C. Staudhammer Slide 6 ANOVA for repeated measures What design does this remind you of?? Example: we measure the response of vegetation in t =3 burning treatments at m= 6 times, with r= 4 replications Source Burn treatment t-1 = 2 Error 1 t(r-1) = 9 Time m-1 = 5 Burn x time (t-1)(m-1) = 10 Experimental Error t(m-1)(r-1) = 45 Total rtm-1 = 71 Degrees of Freedom
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Fal 2007, C. Staudhammer Slide 7 Why not analyze repeated measures experiments as split-plots? ± The treatments are analogous to the main- plot effects ± The measurement times are analogous to the sub-plot effects But… Fal 2007, C. Staudhammer Slide 8 Why not analyze repeated measures experiments as split-plots? (… cont’d) ± In split-plot experiments, sub-plots are randomly assigned Æ
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4b_ mixed mod_pt2 - Motivating texts Advanced Topics in...

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