In Class Project2, R

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\\Project 2\\
#R version 3.3.2 
  
#computing marginal, joint,  and conditional probablities

afterlife<- matrix(c(435,147,375,134),nrow=2,byrow=TRUE);afterlife
dimnames(afterlife)<-listc("Female","Male"),c("Yes","No")) #to look nice
names(dimnames(afterlife))<-c("Gender","Believer")
afterlife 
tot<-sum(afterlife);tot #adds all cells
afterlife/tot #proportions, joint probabilites 
rowtot<-apply(afterlife,1,sum);rowtot #marginal probabilities 
#A[row,columns]
#apply..name of matrix,1 means row/2 means column
coltot<-apply(afterlife,2,sum);coltot
rowpct<-sweep(afterlife,1,rowtot,"/");rowpct #conditional distributions,/means divide row, pi and q
round(rowpct,3) #round to 3 decimals

#difference in proportions, RR, odds, odds ratio
phs<-matrix(c(189,10845,104,10933,ncol=2,byrow=T);phs
dimnames(phs)<-list(Group=c("Placebo","Aspirin"),MI=c("Yes","No")) #to look nice       
phs
prop.test(phs)
#RR=pi1/pi2, RR^=p1/p2
phs.test<-prop.test(phs)
names(phs.test) #all the things you can extract from the test
phs.test$statistic 
phs.test$conf.int
phs.test$estimate #gives a vector
phs.test$estimate[1]/phs.test$estimate[2] #RR
odds<-phs.test$estimate/(1-phs.test$estimate);odds
odds[1]/odds[2] #odds ratio
(phs[1,1]*phs[2,2]/(phs[2,1]*phs[1,2]) #theta hat n11n22/n12n21
phs
theta<-odds[1]/odds[2]
ase<-sqrt(sum(1/phs));ase
logtheta.ci<-log(theta)+c(-1,1)*1.96*are
logtheta.ci
exp(logtheta.ci)
 
#Chi square test, G square test, Fishers exact test
gendercap<-matrix(c(279,73,225,165,47,191),byrow=TRUE,nrow=2)
dimnames(gendercap)<-list(Gender=c("Females","Males"),PartyID=c("Democrat","Independent","Republican"))
gendercap
chisq.test(gendercap)
chisq.test(gendercap,simulate.p.value=TRUE,B=10000)

#Gsqaure test
rtot<-apply(gendercap,1,sum);rtot
ctot<-apply(gendercap,2,sum);ctot
n<-sum(gendercap);n
mu<-rtot%*%t(ctot)/n;mu #matrix multiplication
df<-(nrow(gendercap)-1)*(ncol(gendercap)-1);df 
g<-2*sum(gendercap*log(gendercap/mu));g
pval<-1-pchisq(g,df);pval

#use source() to read file into R
source("gtest.r")
g.test(gendercap)  #helpful for partioning          
            
#Fishers Test
tea<-matrix(c(3,1,1,3), ncol=2)
dimnames(tea)<-list(Poured=c("milk","tea"),Guess=c("milk","tea")
tea
fisher.test(tea)
fisher.test(tea,alternative="greater")

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