18 ANOVA

# 18 ANOVA - Multisample Hypotheses Analysis of Variance...

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Multisample Hypotheses Analysis of Variance Sources of Variation Multiple Comparisons D&B Chapter 11

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Motivation ± Thus far we’ve examined measuring differences between one sample and another ± Examples: ± Experimental ± Treatment and Control ± Observational ± Alternate Conditions ± Alternate Populations
Motivation ± Under those circumstances we conducted a t-test to examin the difference between two means. ± But what if we wish to examine differences across a variety of treatments or conditions?

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Examples ± Continuous or Discrete Data ± Agricultural production vs. amount of rain ± Intellectual impairment vs. level of lead in the blood ± Nominal Data ± Agricultural production vs. variety ± Physiological response vs. drug type ± Response relative to predictor (factor: level)
Blood Lead Concentration Stanford-Binet Intelligence Score 0 5 10 15 20 60 70 80 90 100 110 Continuous-Discrete Data

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Gender Foot size (cm) 22 24 26 28 30 Male Female Nominal Data
Nominal Data Script plot(c(0,3),c(min(females),max(males)),type='n', xlab="Gender",ylab="Foot size (cm)",axes=F) axis(side=2) axis(side=1,at=c(1,2),labels=c("Male","Female")) box() points(jitter(rep(1,length(males))), jitter(males),pch=1) points(jitter(rep(2,length(females))), jitter(females),pch=1)

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Types of Analysis ± Linear Regression ± Gaussian Response with Continuous- Discrete Predictors ± Analysis of Variance ± Gaussian Response with Nominal Predictors
Example: Guayule (wy-oo-lee) ± Rubber Plant ± Parthenium argentatum ± Produces a kind of latex that is hypoallergenic ± Federer (1955) discusses four crop treatments on eight varieties to see the effect on seedling germination ± Help available on guayule data in Splus, but not in R ± Data: guayule.txt http://en.wikipedia.org/wiki/Guayule

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Guayule Data ± guayule ± variety treatment reps plants flats
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## This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell.

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18 ANOVA - Multisample Hypotheses Analysis of Variance...

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