Program2.Question2, R

Program2.Question2

#MATRIX TWO
kicker<-matrix(c(22,4,10,6),ncol=2,byrow=T);kicker
dimnames(kicker)<-list(Strategy=c("No Time-Out","Time-Out"),FielgGoal=c("Success","Failure"))
kicker
rtot<-apply(kicker,1,sum);rtot
ctot<-apply(kicker,2,sum);ctot
kicker.test<-prop.test(kicker)
kicker.test$estimate 
p1<-kicker.test$estimate[1]
p2<-kicker.test$estimate[2]

alpha<-0.05
##Wald Confidence Intervals
se<-sqrt((p1*(1-p1)/rtot[1])+(p2*(1-p2)/rtot[2]))
print("The Wald Confidence Interval:")
exp((p1-p2)+c(-1,1)*1.96*se)

var.wald<-p1*(1-p1)/rtot[1] + p2*(1-p2)/rtot[2]
print("The Wald Confidence Interval 2 :")
p1-p2+qnorm(p=c(alpha/2,1-alpha/2))*sqrt(var.wald)

##Agresti-Caffo Confidence Intervals
print("SUM:")
n<-sum(kicker);n
pit1<-(kicker[1,1]+1)/(kicker[1,]+2)
pit2<-(kicker[2,1]+1)/(kicker[2,]+2)
var.AC<-pit1*(1-pit1)/(kicker[1,]+2) + pit2*(1-pit2)/(kicker[2,]+2)

pit1-pit2+qnorm(p=c(alpha/2,1-alpha/2))*sqrt(var.AC)

##Score Test

##Pearson Chi-Sqaured Test
#chisq.test(kicker)
chisq.test(kicker,simulate.p.value=2,B=10000)

##Likelihood Ratio Test aka  Gsqaure test
#g.test(kicker)

n<-sum(kicker);n
mu<-rtot%*%t(ctot)/n;mu #matrix multiplication
df<-(nrow(kicker)-1)*(ncol(kicker)-1);df 
print("The LRT test statistic:")
g<-2*sum(kicker*log(kicker/mu));g
print("The P-Value of the G^2:")
pval<-1-pchisq(g,df);pval

##Relative Risk and RR Confidence Interval
print("The Relative Risk:")
rr<-kicker.test$estimate[1]/kicker.test$estimate[2];rr ##Relative Risk##
se<-sqrt(((1-p1)/rtot[1]*p1)+((1-p2)/rtot[2]*p2))
logrr.ci<-log(rr)+c(-1,1)*1.96*se
print("95% Relative Risk Confidence Interval:")
exp(logrr.ci)

##Odds Ratio and OR Confidence Interval
odds<-kicker.test$estimate/(1-kicker.test$estimate);odds
odds[1]/odds[2] ##odds ratio
(kicker[1,1]*kicker[2,2])/(kicker[2,1]*kicker[1,2])
kicker
print("The Odds Ratio:")
theta<-odds[1]/odds[2];theta
ase<-sqrt(sum(1/kicker));ase
logtheta.ci<-log(theta)+c(-1,1)*1.96*ase
logtheta.ci
print("The 95% Odds Ratio Confidence Interval:")
exp(logtheta.ci)


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