# NOT RUN {
# Generate 10 observations from a logistic distribution with parameters
# location=7 and scale=2, and test the null hypothesis that the true mean
# is equal to 5 against the alternative that the true mean is greater than 5.
# Use the exact permutation distribution.
# (Note: the call to set.seed() allows you to reproduce this example).
set.seed(23)
dat <- rlogis(10, location = 7, scale = 2)
test.list <- oneSamplePermutationTest(dat, mu = 5,
alternative = "greater", exact = TRUE)
# Print the results of the test
#------------------------------
test.list
#Results of Hypothesis Test
#--------------------------
#
#Null Hypothesis: Mean (Median) = 5
#
#Alternative Hypothesis: True Mean (Median) is greater than 5
#
#Test Name: One-Sample Permutation Test
# (Exact)
#
#Estimated Parameter(s): Mean = 9.977294
#
#Data: dat
#
#Sample Size: 10
#
#Test Statistic: Sum(x - 5) = 49.77294
#
#P-value: 0.001953125
# Plot the results of the test
#-----------------------------
dev.new()
plot(test.list)
#==========
# The guidance document "Supplemental Guidance to RAGS: Calculating the
# Concentration Term" (USEPA, 1992d) contains an example of 15 observations
# of chromium concentrations (mg/kg) which are assumed to come from a
# lognormal distribution. These data are stored in the vector
# EPA.92d.chromium.vec. Here, we will use the permutation test to test
# the null hypothesis that the mean (median) of the log-transformed chromium
# concentrations is less than or equal to log(100 mg/kg) vs. the alternative
# that it is greater than log(100 mg/kg). Note that we *cannot* use the
# permutation test to test a hypothesis about the mean on the original scale
# because the data are not assumed to be symmetric about some mean, they are
# assumed to come from a lognormal distribution.
#
# We will sample from the permutation distribution.
# (Note: setting the argument seed=542 allows you to reproduce this example).
test.list <- oneSamplePermutationTest(log(EPA.92d.chromium.vec),
mu = log(100), alternative = "greater", seed = 542)
test.list
#Results of Hypothesis Test
#--------------------------
#
#Null Hypothesis: Mean (Median) = 4.60517
#
#Alternative Hypothesis: True Mean (Median) is greater than 4.60517
#
#Test Name: One-Sample Permutation Test
# (Based on Sampling
# Permutation Distribution
# 5000 Times)
#
#Estimated Parameter(s): Mean = 4.378636
#
#Data: log(EPA.92d.chromium.vec)
#
#Sample Size: 15
#
#Test Statistic: Sum(x - 4.60517) = -3.398017
#
#P-value: 0.7598
# Plot the results of the test
#-----------------------------
dev.new()
plot(test.list)
#----------
# Clean up
#---------
rm(test.list)
graphics.off()
# }
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