# Exercise 3.11 in Davis, 2002
# Continuation of Exercise 2.3

week <- c(0,2,4,6,8,10,12,14,16,18,19)
m <- matrix(scan("c:\\data.ext\\davis\\kenward.dat"),ncol=13,byrow=T)
group <- m[,1]
calf <- m[,2]
y <- m[,3:13]

# code for graphics, using nlme and lattice libraries
library(nlme)
kenward <- balancedGrouped( y ~ week|calf, matrix(m[,3:13],nrow=60,ncol=11,dimnames=list(calf,week)),
                           labels=list(y="Weight of calves in 19 weeks"))
Group <- rep(group,rep(11,60))
# profile plot
plot(kenward, outer=~as.factor(Group), aspect=1)
# mean plot
kenward.means <- aggregate(kenward$y,list(kenward$week,Group),mean,na.rm=TRUE)
names(kenward.means)[1]<-"Week"
kenward.means$Week <- as.numeric(levels(kenward.means$Week))[kenward.means$Week]
names(kenward.means)[2]<-"Group"
library(lattice)
xyplot(x~Week|Group,kenward.means,ylab="Mean Weight of calves in 19 weeks")

# (a)
results <- matrix(0,nrow=11,ncol=5,byrow=TRUE)
for (i in 1:11) {
  results[i,1] <- week[i]
  ttest <- t.test(y[,i]~group,var.equal=TRUE)
  results[i,2] <- ttest$estimate[1]
  results[i,3] <- ttest$estimate[2]
  results[i,4] <- ttest$statistic
  results[i,5] <- ttest$p.value
  }

# (b) equality between groups
summary(manova(y~group))

# (c) parallel profiles
diff <- matrix(0,nrow=60,ncol=10)
for (i in 1:10)
  diff[,i] <- y[,i]-y[,i+1]
summary(manova(diff~group))