Handout10 - Lecture 10 1. ANOVA example: Rat diets 2....

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Lecture 10 1. ANOVA example: Rat diets 2. Factorial design: 2 £ 2 3. Interactions and interaction plots 4. Factorial design: 2 £ 2 £ 3 5. Adjusted factorial design 1 Generalized Linear Model example: Rat Diets Study by Sabrina Peterson (Food Science and Nutrition) to examine effects on certain liver metabolites over time (7, 30, 60 days) from diets containing: • cruciferous (C) vegetables : broccoli, cabbage, and watercress • apiaceous (A) vegetables: parsnips and celery Four diets: Basal (control), A, C, A+C, with 30 rats assigned to each At 7, 30, 60 days, 10 rats from each diet group will be sacri±ced and liver enzyme activity (MROD) measured. 2
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day diet Frequency|Control |A |AC |C | Total ---------+--------+--------+--------+--------+ 7| 10| 1 0| 1 4 0 ---------+--------+--------+--------+--------+ 30 | 10 | 10 | 10 | 10 | 40 ---------+--------+--------+--------+--------+ 60 | 10 | 10 | 9 | 9 | 38 ---------+--------+--------+--------+--------+ Total 30 30 29 29 118 Slightly unbalanced because 2 rats not measured. 3 2 x 2 Factorial If we consider just the measurements from day 60, we have a 2 £ 2 factorial design: 4 diets (Control, A, C, A+C) deFned by combination of levels of 2 factors: • Cruciferous (cru) : low or high (0/1) • Apiaceous (api): low or high (0/1) Both cru and api are categorical (class) variables. 4
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Part of the data: Obs Plate animal Liver_wt MROD Api Cru day diet 107 15 109 11.32 4.1450 0 1 60 C 108 15 110 14.22 4.2353 0 1 60 C 109 11 112 14.63 3.5352 1 1 60 AC 110 12 113 19.91 2.5222 1 1 60 AC Two different ways to specify the 4 diets: • by diet (0, A, C, AC) • by combinations of cru and api Which is better? 5 Proc GLM code for 2 £ 2 factorial design: Proc GLM data=ph6470.rat_diets; where day=60; use only the 60 day data class api cru ; identify categorical variables model mrod = api cru api*cru; main effects + interaction lsmeans api*cru / pdiff stderr; means api*cru; LSmeans are predicted values: predicted means at each combination of factors. Means are actual averages of data at each combination of factors. 6
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The GLM Procedure Class Level Information Class Levels Values Api 2 0 1 Cru 2 0 1 Number of Observations Read 38 Number of Observations Used 38 7 Like Proc Reg , frst ANOVA table tests all terms combined: Dependent Variable: MROD Sum of Source DF Squares Mean Square F Value Pr > F Model 3 6.44650275 2.14883425 2.84 0.0524 Error 34 25.73230784 0.75683258 Corrected Total 37 32.17881059 R-Square Coeff Var Root MSE MROD Mean 0.200334 25.97334 0.869961 3.349439 This is the ANOVA table For the model MROD = diet; 8
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Type I sums of squares are sequential: each term adjusted for those above.
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This note was uploaded on 11/21/2011 for the course PUBH 6470 taught by Professor Williamthomas during the Fall '11 term at University of Florida.

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Handout10 - Lecture 10 1. ANOVA example: Rat diets 2....

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