# One-sample bootstrap test example using treatment group data from p. 11 of E&T.

set.seed(321)

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

# First I'll do Student's t test.  (I'll do a two-tailed test, using 129 for the 
# null mean.)

t.test( treat, mu = 129 )

# For a bootstrap test, first I'll compute the value of the test
# statistic using the observed sample.

t.stat <- sqrt( 7 )*( mean( treat ) - 129 )/sd( treat )

# Now I'll get replicates of the test statistic based on bootstrap samples drawn
# from the shifted empirical distribution (shifted to be in agreement with the 
# null hypothesis that the mean is 129).

treat.shift <- treat - mean( treat ) + 129
bss <- matrix( sample( treat.shift, 7*4000, replace=T ), nrow=4000 )
mean.rep <- apply( bss, 1, mean )
sd.rep <- apply( bss, 1, sd )
t.rep <- sqrt( 7 )*( mean.rep - 129 )/sd.rep

# Now I'll obtain the estimated lower-tail probability, the estimated upper-tail
# probability, and multiply the smaller of the two by 2 to obtain the p-value.
lower.prob <- length( t.rep[ t.rep <= t.stat ] )/4000 
upper.prob <- length( t.rep[ t.rep >= t.stat ] )/4000 
p.value <- 2*min( lower.prob, upper.prob )

# Here is the upper-tail probability:
upper.prob

# Here is the lower-tail probability:
lower.prob

# The lower-tail probability is close to the value of 0.10 reported in E&T.

# Here is the p-value for the two-tailed test:
p.value

# Johnson's modified t test results in a p-value of 0.2049.