########################################################################
#########                     SBDM  Course                    #########
######  Dr. Ilaria Benedetti - Association among mixed variables ######
########################################################################

#### chi square with  R function

tab<-matrix(c(30,11, 43,39, 1, 35,30, 19, 35),3,3,dimnames = list(c("French", "italian", "other"),
                                                                  c("none","French", "italian")))


chisq <- chisq.test(tab)
chisq 


# Excersise to do: 

# compute chi2 and v-cramer. Provide an interpretation of the results

tab <- matrix(c(14, 47, 160, 172, 12, 12 ),2,3,dimnames = list(c("yes", "no"),
                                                               c("first y.","secondy.","third y.")))
tab


chisq <- chisq.test(tab)
chisq 

chisq 
chisq<- #save the chisq value in an object 

n=nrow(Arthritis)
h=2 #nrow of count
k=3 #ncol of count

# V - cramer 

chi.quad_MAX <- n * min(h - 1,k - 1)
chi.quad_MAX                                                                   

chi.quad_NORM <- chisq / chi.quad_MAX
chi.quad_NORM                                                                  

V <- sqrt(chi.quad_NORM)
V  



######################## Esecise to do  ########################################

## Load vcd package
library(vcd)

## Load Arthritis dataset (data frame)
data(Arthritis)  

str(Arthritis)
summary(Arthritis)

# 1- create a two way table for variables sex and Improved (improvement by gender)
# 2- can we assume that a relationship between gender and improvment level exists?
# 3- compute chi-2 indicator and V-cramer indicator (relative indicator of association)








################   Resolution     ####################


# 1- two way table 
count<-table(Arthritis$Sex, Arthritis$Improved)
count

# 2- 

chisq <- chisq.test(count)
chisq 
chisq<-4.8407 #save in an object only the chisq value

n=nrow(Arthritis)
h=2 #nrow of count
k=3 #ncol of count

# V - cramer 

chi.quad_MAX <- n * min(h - 1,k - 1)
chi.quad_MAX                                                                   

chi.quad_NORM <- chisq / chi.quad_MAX
chi.quad_NORM                                                                  

V <- sqrt(chi.quad_NORM)
V