eye<-c(0.4, 4.6, 2.2, 1.2, 4.5, 5.7, 8.0, 2.1, 4.8, 3.0, 8.8, 11.4, 1.3, 1.4, 2.1, 1.3, 12.5, 2.4, 4.6, 2.8)
plot(density(eye))


##### signed test 
B<-sum(eye >= 5)
binom.test(B, length(eye), 0.5, alternative="less")

####### One sample test 
x<-rnorm(10, mean=6)
wilcox.test(x, mu=5, alternative="less")



####### two-sample test: Wilcoxon Rank Sum test 
# Two-sample test.
## Hollander & Wolfe (1973), 69f.
## Permeability constants of the human chorioamnion (a placental
##  membrane) at term (x) and between 12 to 26 weeks gestational
##  age (y).  The alternative of interest is greater permeability
##  of the human chorioamnion for the term pregnancy.
x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
wilcox.test(x, y, alternative = "greater",
            exact = FALSE, correct = FALSE) # H&W large sample hel# approximation


##### Permutation Test 

x<-rnorm(10, mean=10, sd=1)
y<-rnorm(20 , mean=11.2, sd=1)
group<-rep(c(0,1), c(10, 20))

dat<-data.frame(c(x,y), group)


stripchart(dat[,1] ~ dat[,2], pch=16, method="jitter", jitter=0.2, vertical=TRUE, ylab="Score",  xlab="group", ylim=c(min(dat[,1]), max(dat[,1])))
abline(v=1, col="grey", lty=2)
abline(v=2, col="grey", lty=2)
lines(x=c(0.9, 1.1), rep(mean(dat[dat$group==0,1]),2), col=4)
lines(x=c(1.9, 2.1), rep(mean(dat[dat$group==1,1]),2), col=4)

tout<-t.test(x,y)
names(tout)
tobs<-t.test(x,y)$statistic
perm<-10000
tstar<-rep(NA, perm)
for (i in 1:perm){
	group<-sample(c(rep("x", length(x)), rep("y", length(y))))
	px<-c(x,y)[group=="x"]
	py<-c(x,y)[group=="y"]
	tstar[i]<-t.test(px, py)$statistic
}
plot(density(tstar), main="Permuted Null Distribution")
x<-seq(-4,4, by=0.01)
lines(x,dt(x, df=tout$parameter), lty=2)
pvalue<-mean(abs(tstar) >= abs(tobs))
pvalue