# logic of hypothesis test
# demo of a permutation test
library(ISwR)
data(energy)
energy
help(energy)

by(energy$expend, energy$stature, mean) # equivalent to:  tapply(energy$expend, energy$stature, mean)

obs.diff<-diff(by(energy$expend, energy$stature, mean))

# illustration of a single permutation
sample(1:22)
cbind(energy[sample(1:22),]$expend, energy$stature)

# alternatively, the stature column could be permuted


# 1000 permutations
perm.diff<-numeric(1000)
for(i in 1:1000){
  perm<-sample(1:22)
  perm.diff[i]<-diff(by(energy[perm,]$expend, energy$stature, mean))
}

hist(perm.diff, label=T)
abline(v=obs.diff)

sort(perm.diff)
sum(perm.diff>obs.diff)

quantile(perm.diff, prob=0.95)
quantile(perm.diff, prob=0.995)

#How does the output of the permutation test above compare to the results of a t-test?
t.test(expend ~ stature, data=energy)