##Example 2.1.1
ex.data<-matrix(c(309,191,319,281), ncol=2, byrow=2)
dimnames(ex.data)<-list(Gender=c("Female", "Male"),
Attitude=c("Support","Do not support"))
ex.data

prop.test(ex.data,correct=F) #only applies to I*2 tables
chisq.test(ex.data, correct=F) #apply to general I*J tables

testresult<-prop.test(ex.data,correct=F)
testresult$estimate[1]/testresult$estimate[2]
odds<-testresult$estimate/(1- testresult$estimate)
odds
odds[1]/odds[2] %Odds Ratio%

#expected values
rowsum<-apply(ex.data,1,sum)
colsum<-apply(ex.data,2,sum)
n<-sum(ex.data)
mij<-outer(rowsum,colsum/n,make.dimnames=T)
mij

#residuals
rowp<-rowsum/n #Row marginal prob.
colp<-colsum/n #Column marginal prob.
resid<-(ex.data-mij)/sqrt(mij)
resid

fisher.test(ex.data,alternative="greater")


##logistic regression 
#illustration

mu<--2
sigma<-2

#Examples for f(-2) and F(-2)
dlogis(x = -2, location = mu, scale = sigma)
plogis(q = -2, location = mu, scale = sigma)

win.graph(width = 10, height = 6, pointsize = 12)
par(mfrow = c(1,2))
par(pty="s")

curve(expr = dlogis(x = x, location = mu, scale = sigma), ylab = "f(x)", xlab = "x", xlim = c(-15, 15),
      main = "PDF", col = "red", panel.first = grid(col = "gray", lty = "dotted"), n = 1000)
abline(h = 0)

curve(expr = plogis(q = x, location = mu, scale = sigma), ylab = "F(x)", xlab = "x", xlim = c(-15, 15),
      main = "CDF", col = "red", panel.first = grid(col = "gray", lty = "dotted"), n = 1000)
abline(h = c(0,1))