#Example -  2-Factor Factorial Design 
# Testing hypothesis in two-way ANOVA
library(car)
library(ggplot2)
#Set working directory
setwd("~/Dropbox/ISI SCB/Data sets")

# read in csv file
life <-read.csv("lifetime.csv", TRUE)
Lifetime <- life$Lifetime
Material <- life$Material
Temperature <-life$Temperature

#boxplots
ggplot(life, aes(x=Temperature, y=Lifetime, fill=Material), fixed=TRUE) +
  geom_boxplot()

interaction.plot(Temperature,Material,Lifetime, type ="b", pch=c(19, 17, 15),
                 col=c("blue","red","green"),fixed=TRUE)


#Two-way ANOVA
life.aov<- aov(Lifetime~Material+Temperature+Material:Temperature)
summary(life.aov)

#Two-way ANOVA
life.aov<- aov(Lifetime~Material*Temperature)
summary(life.aov)


#Multiple Comparisons
life.tukey <- TukeyHSD(life.aov)
life.tukey
plot(life.tukey)

#residuals and fitted values of the model
res  <- life.aov$residuals
fit <- life.aov$fitted.values
#residual plot to assess constant variance assumption
plot(fit,res, main="Residual Plot",xlab= "Fitted Values", ylab="Residuals")

#Test constant variance assumption
leveneTest(Lifetime~Material*Temperature)

#assess normality assumption
qqnorm(res, ylab = "Residuals Sample Quantiles")
shapiro.test(res)
hist(res)