# Permutation test example using mouse data from p. 11 of E&T.

set.seed(321)

survival <- c(94,197,16,38,99,141,23,52,104,146,10,51,30,40,27,46)

obs.diff.means <- mean( survival[1:7] ) - mean( survival[8:16] )
obs.diff.meds <- median( survival[1:7] ) - median( survival[8:16] )

diff.means <- numeric()
diff.meds <- numeric()

for ( i in 1:40000 ) {

    perm <- sample( survival, 16, replace=F )
    diff.means[i] <- mean( perm[1:7] ) - mean( perm[8:16] ) 
    diff.meds[i] <- median( perm[1:7] ) - median( perm[8:16] )
  
  }

hist( diff.means )

p <- length( diff.means[ diff.means >= obs.diff.means ] )/40000 
# one-sided test p-values (difference in sample means):
p

pm.part <- 1.96*sqrt( p*( 1 - p )/40000 )
ucb <- p + pm.part
lcb <- p - pm.part
# Here are confidence bounds for the exact p-value:
lcb; ucb

# one-sided test p-values (difference in sample medians):
length( diff.meds[ diff.meds >= obs.diff.meds ] )/40000

#
hist( diff.meds )

# Now I'll do Student's two-sample t test.
 
treat <- c(94,197,16,38,99,141,23)
control <- c(52,104,146,10,51,30,40,27,46)
 
t.test( treat, control, alternative="greater", var.equal=T )