# R-Code from March 29th.  

#We "examined" the Titanic data with the 5 Ws deducible from information here: 

#http://www.encyclopedia-titanica.org/manifest.php?q=1%22%22

 #We have (imagined!) breaking the  community up into three categories via the  three variables Gender, Survival, Class/Crew.

#Legend

#F=Female passengers
#M=Male passengers
#A=Alive, i.e. survivors
#D=Dead, i.e.victims
#1=First class  passengers
#2=Second class  passengers
#3=Third class  passengers
#c=Crew

###################
# Our first contingency table! 

# Rows F,M
# Columns A, D

#The table:

A=rbind(
c(266,500),
c(444,991))

# Type A to see it!

# we can compute the margins as follows... 

# The Gender margin:

M1=margin.table(A,1) 

# The survival margin:

M2=margin.table(A,2) 

#################
#Here is the example in the book.

# Rows A, D
# Columns 1, 2, 3, C

A=rbind(
c(202,118,178,212),
c(123,167,528,673))
M1=margin.table(A,1) 
M2=margin.table(A,2)

# We can use this contingency table and it's margins to produce the possible  Relative Frequency tables with the distributions conditioned on:

# 1. Survival

F1=diag(1/M1)%*%A 

#2. Class/Crew.

F2=A%*%diag(1/M2)

#Exercise: Figure out what diag(1/M2) did to M2.  Why was this useful to us?

##################

# We can plot the percent of each Class/Crew who Survived.

barplot(F2[1,],names.arg=c("First","Second","Third","Crew"),main="Percent Survival by Class",col=rep('blue',4))

# Exercise: Use R to decide what F2[1,] does to F2. 

# quartz() tells the computer to make a new graph. 

quartz()

# We can compare the Survivors by Class

pie(F1[1,],labels=c("First","Second","Third","Crew"),main="Class Breakdown for Survivors")

# With the Victims by Class.

quartz()

pie(F1[2,],labels=c("First","Second","Third","Crew"),main="Class breakdown for Victims")

#They are clearly not independent variables hence are associated. 

# Exercise: Change the tiles and category labels.