DF = data.frame(
    type=c( rep( 'Snoopy', 6 ), rep( 'Quick', 6 ), rep( 'Mrs. Good', 6 ) ),
    data=c( 0.5, 7.3, 1.1, 2.7, 5.5, 4.3, 2.5, 1.8, 3.6, 5.2, 1.2, 0.7, 3.3, 1.5, 0.4, 4.8, 2.2, 1.0 )
)

# The classical ANOVA test (from R in Action EPage 234)
#
fit = aov( data ~ type, data=DF )
print( sprintf("Classical ANOV ") )
print(summary(fit))

#
# To study the main effects of brand we will apply a permuation test:
#
source('utils.R')

F = compute_F( DF$type, DF$data )
set.seed(1234)
B = 100 # the sumber of bootstraps to run
all_Fs = rep( NA, B ) # the bootstrap values of the F
for( bi in 1:B ){
    all_Fs[bi] = compute_F( DF$type, sample(DF$data) )
}

plot( density( all_Fs ), xlab="statistic", main="" )
grid()
abline(v=F, col='red')

alpha = sum( all_Fs >= F ) / B
print( sprintf("main effects for type (B= %d): prob. type I error: %10.6f", B, alpha) )