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

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
Type I sums of squares are sequential: each term adjusted for those above.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 18

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online