# Section 4.2 examples:


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# Section 4.2 R examples
#
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##### Chi-square test of probabilities:

# Test score data:

test.score.data <- matrix(c(6,14,17,9,30,32,17,3), nrow=2, ncol=4, byrow=TRUE, 
dimnames = list(c("Private", "Public"), c("Low", "Marginal", "Good", "Excellent")))

# Printing the 2 by 4 table:

as.table(test.score.data)

# A quick way to get expected cell counts and verify large-sample assumption is met:

expected.counts <- (apply(test.score.data,1,sum) %o% apply(test.score.data,2,sum))/sum(test.score.data)
print(expected.counts)

# using the chisq.test() function in R:

chisq.test(test.score.data, correct=FALSE)


##### Chi-square test of independence:

# Snoring/heart disease data:


snore.heart.data <- matrix(c(24,35,51,1355,603,416), nrow=2, ncol=3, byrow=TRUE, 
dimnames = list(c("Yes", "No"), c("Never", "Occasionally", "~ Every Night")))

# Printing the 2 by 3 table:

as.table(snore.heart.data)

# A quick way to get expected cell counts and verify large-sample assumption is met:

expected.counts <- (apply(snore.heart.data,1,sum) %o% apply(snore.heart.data,2,sum))/sum(snore.heart.data)
print(expected.counts)


# We test for independence of the two classifications
# using the chisq.test() function in R:

chisq.test(snore.heart.data, correct=FALSE)


##### Exact test on r-by-c table with fixed marginals:

# 3-by-3 bank data:

bank.3.data <- matrix(c(0,5,1,2,3,0,2,0,1), nrow=3, ncol=3, byrow=TRUE, 
dimnames = list(c("White", "Black", "Asian"), c("AcctRep", "Teller", "DataAnalyst")))

# Printing the 3 by 3 table:

as.table(bank.3.data)

# using the fisher.test() function in R:

fisher.test(bank.3.data)