#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
#
#-----

corner = c( 10, 16, 23, 23, 19, 16, 12, 18 )
side = c( 7, 10, 24, 18, 15, 18, 11, 14 )

# We lump both data sets together and then randomly select the items to be in the "corner" group
# (while the others will then be in the "side" group):
#

data = c( corner, side )

# The statistic is the sum of the responses in the corner sample:
#
X = sum( corner )

# Generate the needed combinations of the total data and apply our statistic function to each combination:
Perm_Test_Data = combn( data, length(corner), sum )

#postscript("../../WriteUp/Graphics/Chapter3/ex_6_permutation_test.eps", onefile=FALSE, horizontal=FALSE) 
hist( Perm_Test_Data, breaks=20,
      xlab="sum of samples labeled corner",
      main="Possible Values for the Test Statistic under the Null Hypothesis" )
abline( v=X, col='red' )
#dev.off()

# What is the probability of getting the value obtained (or a larger one):
#
alpha = sum( Perm_Test_Data >= X ) / length( Perm_Test_Data )
print( sprintf("alpha (prob. type I error): %10.6f", alpha) )