################################
#
# Section 4.4 R examples
#
################################

## Cramer's Coefficient

# Copy and paste this function first:
CramerV <- function(xtable){
V<-sqrt(chisq.test(xtable, correct = FALSE)$statistic / (sum(xtable) * min(dim(xtable) - 1 )))
names(V) <- NULL
return(V)
}

# Example 1:

test.score.data <- matrix(c(6,14,17,9,30,32,17,3), nrow=2, ncol=4, byrow=TRUE, 
dimnames = list(c("Private", "Public"), c("Low", "Marginal", "Good", "Excellent")))

CramerV(test.score.data)

# Example 2:

snore.heart.data <- matrix(c(24,35,51,1355,603,416), nrow=2, ncol=3, byrow=TRUE, 
dimnames = list(c("Yes", "No"), c("Never", "Occasionally", "~ Every Night")))

CramerV(snore.heart.data)


## Phi coefficient:

# Copy and paste this function first:
Phi <- function(xtable){
phii<-(xtable[1,1]*xtable[2,2]-xtable[1,2]*xtable[2,1])/sqrt(prod(apply(xtable,1,sum),apply(xtable,2,sum)) )
names(phii) <- NULL
return(phii)
}

# Example 3:

Table223A <- matrix(c(28,0,5,7), nrow=2, ncol=2, byrow=TRUE, 
dimnames = list(c("DarkM", "LightM"), c("DarkF","LightF")))

Phi(Table223A)

Table223B <- matrix(c(21,7,12,0), nrow=2, ncol=2, byrow=TRUE, 
dimnames = list(c("DarkM", "LightM"), c("DarkF","LightF")))

Phi(Table223B)

Table223C <- matrix(c(23,5,10,2), nrow=2, ncol=2, byrow=TRUE, 
dimnames = list(c("DarkM", "LightM"), c("DarkF","LightF")))

Phi(Table223C)

# Example 4:

haireye22 <- matrix(c(1168,1130,573,2512), nrow=2, ncol=2, byrow=TRUE, 
dimnames = list(c("LightE", "DarkE"), c("LightH","DarkH")))

as.table(haireye22)

Phi(haireye22)



################################
#
# Section 4.6 R examples
#
################################

## Cochran's Test:


Cochran.Test <- function(xtable){
c <- ncol(xtable)
r <- nrow(xtable)
N <- sum(xtable)
test.stat <- (c*(c-1)*sum(apply(xtable,2,sum)^2) - (c-1)*N*N)/(c*N-sum(apply(xtable,1,sum)^2))
p.value <- pchisq(test.stat, df=(c-1), lower=F)
out <-list(test.stat,p.value)
return(out)
}

climbs<-matrix(c(1,1,0,
1,0,1,
0,0,1,
0,1,1,
1,0,1)
,nrow=5,ncol=3,byrow=T)


Cochran.Test(climbs)