## R-Script to Exercise 5

## Task 1

##Read in the data.


paint <- read.table(file="http://stat.ethz.ch/Teaching/Datasets/paint.txt",header=TRUE)                       

## a)


plot(paint$BATCH[paint$SAMPLE==1],paint$MOISTURE[paint$SAMPLE==1],col=2,)
points(paint$BATCH[paint$SAMPLE==2],paint$MOISTURE[paint$SAMPLE==2],col="blue")


paint$SAMPLE <- as.factor(paint$SAMPLE)
paint$BATCH <- as.factor(paint$BATCH)

## d)

mod1 <- aov(MOISTURE~BATCH/SAMPLE,data=paint)
summary(mod1)

mod2 <- aov(MOISTURE~BATCH+Error(SAMPLE%in% BATCH),data=paint)
summary(mod2)


## Task 2

## ## Read in the data.

peanut <- read.table(file="http://stat.ethz.ch/Teaching/Datasets/Peanut.txt",header=TRUE)                       

peanut$Row <- as.factor(peanut$Row)
peanut$Column <- as.factor(peanut$Column)
peanut$Treatment <- as.factor(peanut$Treatment)

## a)

par(mfrow=c(2,2))
plot(Yield ~ Treatment+Row+Column, data=peanut)

## b)

modP1 <- aov(Yield ~ Treatment+Row+Column, data=peanut)
summary(modP1)

## c)

TukeyHSD(modP1,"Treatment", conf.level=0.90)


peanut2 <- read.table(file="http://stat.ethz.ch/Teaching/Datasets/Peanut2.txt",header=TRUE)

peanut2$Row <- as.factor(peanut2$Row)
peanut2$Column <- as.factor(peanut2$Column)
peanut2$Treatment <- as.factor(peanut2$Treatment)
peanut2$Rep <- as.factor(peanut2$Rep)

## e)

modP2 <- aov(Yield ~ Treatment+Rep/(Row+Column), data=peanut2)
summary(modP2)

TukeyHSD(modP2,"Treatment", conf.level=0.90)


## Task 3

##Read in the data.

tennis <- read.table(file="http://stat.ethz.ch/Teaching/Datasets/TENNIS.dat")
names(tennis)=c("id","age","sex","order","max1","twelve1","ave1","overall1","max2","twelve2","ave2","overall2","max3","twelve3","ave3","overall3")
head(tennis)
for (i in 3:16) 
tennis[,i][tennis[,i]==9]=NA

diff.max=tennis$max1-tennis$max3
diff.max[tennis$order==2]=-diff.max[tennis$order==2]
plot(diff.max)
abline(h=0,col=2,lty=2)
summary(diff.max)
t.test(diff.max)
wilcox.test(diff.max)

diff.twelve=tennis$twelve1-tennis$twelve3
diff.twelve[tennis$order==2]=-diff.twelve[tennis$order==2]
plot(diff.twelve)
abline(h=0,col=2,lty=2)
summary(diff.twelve)
t.test(diff.twelve)
wilcox.test(diff.twelve)

diff.ave=tennis$ave1-tennis$ave3
diff.ave[tennis$order==2]=-diff.ave[tennis$order==2]
plot(diff.ave)
abline(h=0,col=2,lty=2)
summary(diff.ave)
t.test(diff.ave)
wilcox.test(diff.ave)

diff.overall=tennis$overall1-tennis$overall3
diff.overall[tennis$order==2]=-diff.overall[tennis$order==2]
plot(diff.overall)
abline(h=0,col=2,lty=2)
summary(diff.overall)
t.test(diff.overall)
wilcox.test(diff.overall)

# degree of pain while on Motrin significantly better
# than degree of pain on placebo  for all four pain measurements

# Anova  approach for max, ave, twelve and overall
# Example for max:

tennis.max=reshape(tennis[,c(1:5,9,13)],varying=c("max1","max2","max3"),idvar="id", timevar="period",v.names="max",direction="long")
tennis.max$Treatment[tennis.max$order==1 & tennis.max$period==1]="Motrin"
tennis.max$Treatment[tennis.max$period==2]="Washout"
tennis.max$Treatment[tennis.max$order==1 & tennis.max$period==3]="Placebo"
tennis.max$Treatment[tennis.max$order==2 & tennis.max$period==3]="Motrin"
tennis.max$Treatment[tennis.max$order==2 & tennis.max$period==1]="Placebo"

tennis.max$Treatment=factor(tennis.max$Treatment)
tennis.max$id=factor(tennis$id)

tennis.max$sex[tennis.max$sex==9]=NA
tennis.max$sex=factor(tennis$sex)
levels(tennis.max$sex)=c("male","female")
tennis.max$period=factor(tennis.max$period)

mod1=aov(max~id+period+Treatment,data=tennis.max[tennis.max$period!=2,])
summary(mod1)
model.tables(mod1,type="means")



# significant difference between Motrin and Placebo


# Is there any carry-over effect?

# If there is a lasting effect of Motrin, the treatment difference in group A is smaller
# than in group B, in other words the average response in group A is larger than  in
# group B.

mod2=aov(max~order,data=tennis.max[tennis.max$period!=2,])
summary(mod2)

# This not the case.
# Another possibility: Are there any differences in the washout responses?

mod3=aov(max~order,data=tennis.max[tennis.max$period==2,])
summary(mod3)

# No. 

# Or: Is the treatment difference larger in period 1 than in period 2?