# NOT RUN {
# Generate 10 observations from a binomial distribution with parameters
# size=1 and prob=0.3, and 20 observations from a binomial distribution
# with parameters size=1 and prob=0.5. Test the null hypothesis that the
# probability of "success" for the two distributions is the same against the
# alternative that the probability of "success" for group 1 is less than
# the probability of "success" for group 2.
# (Note: the call to set.seed allows you to reproduce this example).
set.seed(23)
dat1 <- rbinom(10, size = 1, prob = 0.3)
dat2 <- rbinom(20, size = 1, prob = 0.5)
test.list <- twoSamplePermutationTestProportion(
dat1, dat2, alternative = "less")
#----------
# Print the results of the test
#------------------------------
test.list
#Results of Hypothesis Test
#--------------------------
#
#Null Hypothesis: p.x - p.y = 0
#
#Alternative Hypothesis: True p.x - p.y is less than 0
#
#Test Name: Two-Sample Permutation Test
# Based on Differences in Proportions
# (Fisher's Exact Test)
#
#Estimated Parameter(s): p.hat.x = 0.60
# p.hat.y = 0.65
#
#Data: x = dat1
# y = dat2
#
#Sample Sizes: nx = 10
# ny = 20
#
#Test Statistic: p.hat.x - p.hat.y = -0.05
#
#P-value: 0.548026
#----------
# Plot the results of the test
#------------------------------
dev.new()
plot(test.list)
#----------
# Compare to the results of fisher.test
#--------------------------------------
x11 <- sum(dat1)
x21 <- length(dat1) - sum(dat1)
x12 <- sum(dat2)
x22 <- length(dat2) - sum(dat2)
mat <- matrix(c(x11, x12, x21, x22), ncol = 2)
fisher.test(mat, alternative = "less")
#Results of Hypothesis Test
#--------------------------
#
#Null Hypothesis: odds ratio = 1
#
#Alternative Hypothesis: True odds ratio is less than 1
#
#Test Name: Fisher's Exact Test for Count Data
#
#Estimated Parameter(s): odds ratio = 0.8135355
#
#Data: mat
#
#P-value: 0.548026
#
#95% Confidence Interval: LCL = 0.000000
# UCL = 4.076077
#==========
# Rodricks (1992, p. 133) presents data from an experiment by
# Graham et al. (1975) in which different groups of rats were exposed to
# various concentration levels of ethylene thiourea (ETU), a decomposition
# product of a certain class of fungicides that can be found in treated foods.
# In the group exposed to a dietary level of 250 ppm of ETU, 16 out of 69 rats
# (23%) developed thyroid tumors, whereas in the control group
# (no exposure to ETU) only 2 out of 72 (3%) rats developed thyroid tumors.
# If we use Fisher's exact test to test the null hypothesis that the proportion
# of rats exposed to 250 ppm of ETU who will develop thyroid tumors over their
# lifetime is no greater than the proportion of rats not exposed to ETU who will
# develop tumors, we get a one-sided upper p-value of 0.0002. Therefore, we
# conclude that the true underlying rate of tumor incidence in the exposed group
# is greater than in the control group.
#
# The data for this example are stored in Graham.et.al.75.etu.df.
# Look at the data
#-----------------
Graham.et.al.75.etu.df
# dose tumors n proportion
#1 0 2 72 0.02777778
#2 5 2 75 0.02666667
#3 25 1 73 0.01369863
#4 125 2 73 0.02739726
#5 250 16 69 0.23188406
#6 500 62 70 0.88571429
# Perform the test for a difference in tumor rates
#-------------------------------------------------
Num.Tumors <- with(Graham.et.al.75.etu.df, tumors[c(5, 1)])
Sample.Sizes <- with(Graham.et.al.75.etu.df, n[c(5, 1)])
test.list <- twoSamplePermutationTestProportion(
x = Num.Tumors, y = Sample.Sizes,
x.and.y="Number Successes and Trials", alternative = "greater")
#----------
# Print the results of the test
#------------------------------
test.list
#Results of Hypothesis Test
#--------------------------
#
#Null Hypothesis: p.x - p.y = 0
#
#Alternative Hypothesis: True p.x - p.y is greater than 0
#
#Test Name: Two-Sample Permutation Test
# Based on Differences in Proportions
# (Fisher's Exact Test)
#
#Estimated Parameter(s): p.hat.x = 0.23188406
# p.hat.y = 0.02777778
#
#Data: x = Num.Tumors
# n = Sample.Sizes
#
#Sample Sizes: nx = 69
# ny = 72
#
#Test Statistic: p.hat.x - p.hat.y = 0.2041063
#
#P-value: 0.0002186462
#----------
# Plot the results of the test
#------------------------------
dev.new()
plot(test.list)
#==========
# Clean up
#---------
rm(test.list, x11, x12, x21, x22, mat, Num.Tumors, Sample.Sizes)
#graphics.off()
# }
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