Chapter 28 ANOVA: analysis of variance

to perform the analysis of variance performed in class you need to load the lecture19.Rdata file

load("files/lecture19.Rdata")
attach(bw.data)

## The following object is masked _by_ .GlobalEnv:
## 
##     bw

28.1 Performing ANOVA in R

#use aov() to perform ANOVA
aov(bw~genotype)

## Call:
##    aov(formula = bw ~ genotype)
## 
## Terms:
##                 genotype Residuals
## Sum of Squares  507989.9  475210.6
## Deg. of Freedom        2        12
## 
## Residual standard error: 198.9997
## Estimated effects may be unbalanced

#wrap it in summary() to get a nicer output
summary(aov(bw~genotype))

##             Df Sum Sq Mean Sq F value Pr(>F)  
## genotype     2 507990  253995   6.414 0.0127 *
## Residuals   12 475211   39601                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#plot bw data as a simple dot plot
plot(c(bw[1:5], bw[11:15], bw[6:10]), pch=1, lwd=3, col=c(2,2,2,2,2,4,4,4,4,4,1,1,1,1,1), ylim=c(2800,4100), xlab="", ylab="Birthweight (g)", xaxt='n', ann=FALSE)

par(mfrow = c(1,3))
#plot bw data as a simple dot plot 
plot(c(bw[1:5], bw[11:15], bw[6:10]), pch=20, lwd=1, col=c(2,2,2,2,2,4,4,4,4,4,1,1,1,1,1), ylim=c(2800,4100), xlab="", ylab="Birthweight (g)", xaxt='n', ann=FALSE, cex.axis=1.5, cex=2)
plot(c(bw[1:5], bw[11:15], bw[6:10]), pch=20, lwd=1, col=c(2,2,2,2,2,4,4,4,4,4,1,1,1,1,1), ylim=c(2800,4100), xlab="", ylab="Birthweight (g)", xaxt='n', ann=FALSE, cex.axis=1.5, cex=2)
plot(c(bw[1:5], bw[11:15], bw[6:10]), pch=20, lwd=1, col=c(2,2,2,2,2,4,4,4,4,4,1,1,1,1,1), ylim=c(2800,4100), xlab="", ylab="Birthweight (g)", xaxt='n', ann=FALSE, cex.axis=1.5, cex=2)

28.2 The F distribution

par(mfrow=c(1,2))

#Plot an F distribution
nd <- seq(0,7,0.1)
y <- df(nd,2,20)
plot(nd,y,type="l", xlab="F", ylab="probability", ylim=c(0,1))

y <- df(nd,4,20)
plot(nd,y,type="l", xlab="F", ylab="probability", ylim=c(0,1))

y <- df(nd,6,20)
plot(nd,y,type="l", xlab="F", ylab="probability", ylim=c(0,1))

y <- df(nd,1,20)
plot(nd,y,type="l", xlab="F", ylab="probability", ylim=c(0,1))

y <- df(nd,100,1000)
plot(nd,y,type="l", xlab="F", ylab="probability")