assumptions.R

#
# Start with Basic ANOVA
#
data <- read.table("CH18TA05.txt",col.names=c("failure","loc","observation"))
attach(data)
locf <- factor(loc,levels=c(1:3),labels=c("Loc 1","Loc 2","Loc 3"))
result <- lm(failure~locf)
anova(result)
boxplot(failure~locf)

names(result)
plot(result$fited.values,result$residuals)
plot(result$fit,result$res)
plot(result,1)

install.packages("car")
library(car)

qqPlot(result)

leveneTest(result,center=mean)            # Levene Test
leveneTest(result,center=median)          # Brown-Forsythe

#
# Ratios:  Which is the most consistent
#
tapply(failure,locf,var)/tapply(failure,locf,mean)  # Square root
tapply(failure,locf,sd)/tapply(failure,locf,mean)   # Natural Log
tapply(failure,locf,sd)/tapply(failure,locf,mean)^2 # 1/Y

boxplot(log(failure)~locf)
res2 <- lm(log(failure)~locf)
anova(res2)

qqPlot(res2)
plot(res2,1)

# Box Cox
boxCox(result)

res3 <- lm(failure^.1~locf)
anova(res3)
qqPlot(res3)


#
# Does this effect the Tukey Test?
#

TukeyHSD(aov(result),conf.level=.95)
TukeyHSD(aov(res3),conf.level=.95)

#
# Does it effect fit.contrast?
#

library(gmodels)
fit.contrast(result,locf,c(-1,1,0))
fit.contrast(res3,locf,c(-1,1,0))

#
# Confidence interval for Location 1
#

(mu.i <- tapply(failure,locf,mean))
n.i <- tapply(failure,locf,length)
anova(result)
mse <- 6353.2

mu.i[1] + c(-1,1)*qt(.975,12)*sqrt(mse/n.i[1])

# With transformation

(mu.i <- tapply(failure^.1,locf,mean))
n.i <- tapply(failure^.1,locf,length)
anova(res3)
mse <- 0.028894

mu.i[1] + c(-1,1)*qt(.975,12)*sqrt(mse/n.i[1])
(mu.i[1] + c(-1,1)*qt(.975,12)*sqrt(mse/n.i[1]))^(1/.1)

library(gplots)

(se.i <- sqrt(mse/n.i))

barplot2(mu.i^(1/.1),plot.ci=TRUE,ci.l=(mu.i-qt(.975,24)*se.i)^(1/.1),ci.u=(mu.i+qt(.975,24)*se.i)^(1/.1))


#
# Arcsin Transformation
# 

data2 <- read.csv("seed.csv")
attach(data2)
boxplot(p.germ~treatment)

result <- lm(p.germ~factor(treatment))
anova(result)
qqPlot(result)
leveneTest(result,center=mean)
leveneTest(result,center=median)

p.germ.t <- 2*asin(sqrt(p.germ))
boxplot(p.germ.t~treatment)

result <- lm(p.germ.t~factor(treatment))
anova(result)
qqPlot(result)
leveneTest(result,center=mean)
leveneTest(result,center=median)