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### Section 5.11 Examples
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## Randomization Test with Two Independent Samples

withDH <- c(6,2,3,6,8,1,3,7,6,4,4,12,5,6,13,6,9,5,6,7,4,3,2,5,5,6,14,14,7,0)
withoutDH <- c(1,5,5,4,7,2,6,2,9,2,8,8,2,10,4,4,3,4,1,9,3,5,1,3,3,3,5,2,7,2)

T1.obs <- sum(withDH)

combined.sample <- c(withDH, withoutDH)

num.perm <- 50000
permutation.matrix <- matrix(0,ncol=length(combined.sample),nrow=num.perm)

for (i in 1:num.perm){
# getting random permutation of combined.sample:
permutation.matrix[i,] <- sample(combined.sample)
}

null.T1.distn <- rowSums(permutation.matrix[,(1:length(withDH))])

p.value <- mean(null.T1.distn >= T1.obs)  # For an upper-tailed test

print(p.value)

## Randomization Test with Two Paired Samples

drugA <- c(74,55,61,41,53,74,52,31,50,58,54,53,69,60,61,54,57)

drugB <- c(63,58,49,47,50,69,67,40,44,38,56,38,47,41,46,47,44)

diffs <- drugA - drugB

diffs <- diffs[diffs != 0]  # removing any "zero differences"

T2.obs <- sum(diffs[diffs>0])

num.perm <- 50000

permutation.matrix <- matrix(0,ncol=length(diffs),nrow=num.perm)

for (i in 1:num.perm){
# getting random permutation of signs for vector of differences:
permutation.matrix[i,] <- sample(c(-1,1),replace=T,size=length(diffs))*diffs
}

null.T2.distn <- rowSums(pmax(permutation.matrix,0))


p.value <- 2*min( mean(null.T2.distn >= T2.obs), mean(null.T2.distn <= T2.obs) )  # For a two-tailed test

print(p.value)