## MB Baseball data
## March 10, 2008

## humid, dry, control
dry <- c(103, 111, 100, 112, 106)
dry.50 <- c(101, 102,  99,  92, 90)
humid <-  c(93, 85, 94, 95, 87)

y <- c(dry,  dry.50, humid)
x <- c(rep("dry", 5), rep("dry.50", 5), rep("humid", 5))

## do the F-test
anova(lm(y~as.factor(x)))

## check the assumptions
# normality
options(contrasts = c("contr.sum", "contr.poly"))
mod.lm <- lm(y~as.factor(x))

par(mfrow=c(1,2))
hist(mod.lm$res)
qqnorm(mod.lm$res); qqline(mod.lm$res)

## variances
s.sq.i <- tapply(y,x,var)
max(s.sq.i)/min(s.sq.i)


## Get 95% CIs
mu.i <- tapply(y,x,mean)
s.sq <- anova(lm(y~as.factor(x)))[2,3]
se <- sqrt(s.sq/5)
cbind(mu.i - se*qt(1-0.05/2, 15-3),
mu.i + se*qt(1-0.05/2, 15-3))


## Get all pairwise comparisons
K <- matrix(c(1,-1,0,
			  1,0,-1,
			  0,1,-1),3,3, byrow=T)

K
			  
C.hat <- K%*%mu.i
se.1 <- sqrt(s.sq*sum(K[1,]^2/5)) 
se.2 <- sqrt(s.sq*sum(K[2,]^2/5)) 
se.3 <- sqrt(s.sq*sum(K[3,]^2/5)) 

cbind(C.hat - c(se.1,se.2,se.3)*qt(1-(0.05/3)/2, 15-3),
C.hat + c(se.1,se.2,se.3)*qt(1-(0.05/3)/2, 15-3))


## check assumptions
par(mfrow=c(2,2))
qqnorm(dry); qqline(dry)
qqnorm(humid); qqline(humid)
boxplot(dry, col="yellow", ylim=c(80,115))
boxplot(humid, col="yellow", ylim=c(80,115))

## do the test
t.test(dry, humid, var=T)
t.test(dry, humid, var=T, alt="greater")


## Corked Bat
uncorked <- c(77.2, 79.7, 79.7, 80.4)
corked <- c(39.3, 37.4, 38.8, 37.8)

par(mfrow=c(2,2))
qqnorm(corked); qqline(corked)
qqnorm(uncorked); qqline(uncorked)
boxplot(corked, col="yellow", ylim=c(35,81))
boxplot(uncorked, col="yellow", ylim=c(35,81))

## do the test
t.test(corked, uncorked, var=T)

## (paired t-test)
## The Slide

run <- c(3.624, 4.076, 4.13)
slide <- c(3.572, 3.976, 3.93)
id <- c(Tory, Jamie, Grant)

t.test(run,slide,paired=T, var.equal=T)