## Comparing two proportions ##

# Table 2.3, p. 27 (attack v. no attack)

x<-c(189,104) # placebo, aspirin
n<-c(11034,11037)

# test H0:p1=p2 (equal probabilities of heart attack)
prop.test(x,n,p=c(.5,.5))
prop.test(x,n)$p.value

# Test H0:p1=p2 v. H1:p1>p2
prop.test(x,n,alt="greater")$p.value

# sample difference of proportions:
temp<-prop.test(x,n)  
names(temp$estimate)<-NULL  # optional
temp$estimate[[1]]-temp$estimate[[2]]

# relative risk
temp$estimate[[1]]/temp$estimate[[2]]

# odds ratio
x[1]*(n[2]-x[2])/(x[2]*(n[1]-x[1]))