# Chapter 10 R examples

surgery = matrix(c(41,8,15,11), nrow=2)
colnames(surgery) = c("Real", "Sham")
rownames(surgery) = c("Success", "No Success")

# For a directional test, need to divide the given P-value from chisq.test by 2 to get the real P-value:
chisq.test(surgery, correct=FALSE)

# The prop.test function gives you the P-value of the directional test directly:
prop.test(surgery, correct=FALSE,alternative = "greater")



testing = matrix(c(9,52,8,51), nrow=2)
colnames(testing) = c("Female","Male")
rownames(testing) = c("HIV Test", "No HIV Test")
testing            

chisq.test(testing, correct=FALSE)

# Fisher's exact test:

flu = matrix(c(15,13,3,10), nrow=2)
fisher.test(flu, alternative="greater")

fisher.test(flu, alternative="two.sided")
# To get the two-sided test, could simply type:  fisher.test(flu)

# Large-sample CI for p1-p2:

success = c(274, 72)
total = c(347, 298)
prop.test(success, total, conf.level=0.95, correct=FALSE)