# Simple example of the percentile interval, based on the sample of 7
# observations of the Treated mice.  (Data on p. 11 of E&T.)

treatment <- c(94, 197, 16, 38, 99, 141, 23)

set.seed(321)

# I'll get a 90% percentile interval for the mean of the treatment dist'n.
bss <- matrix( sample( treatment, 7*1999, replace=T ), nrow=1999 )
mean.rep <- apply( bss, 1, mean )
sorted.mean.rep <- sort( mean.rep )

# upper confidence bound:
sorted.mean.rep[1900]
# lower confidence bound:
sorted.mean.rep[100]
# Not too different from the interval (49.7, 126.7) given in Ch. 13 of E&T.

# point estimate (sample mean):
mean( treatment )

# Let's compare with a traditional t interval.
t.result <- t.test( treatment, conf.level=0.90 )
t.result$conf.int

# Let's further compare with a bootstrap-t interval.
sd.rep <- apply( bss, 1, sd )
z.rep <- ( mean.rep - mean( treatment ) )/( sd.rep/sqrt(7) )
sorted.z.rep <- sort( z.rep )
# upper confidence bound:
mean( treatment ) - sorted.z.rep[100]*sd( treatment )/sqrt( length( treatment ) )
# lower confidence bound:
mean( treatment ) - sorted.z.rep[1900]*sd( treatment )/sqrt( length( treatment ) )