##### SCA-41
##### 
##### Chi-Square Test of Independence
##### 

### This gives a few examples of the analysis process for testing
### for independence between two categorical variables



### Preamble

source("http://rfs.kvasaheim.com/stat200.R")


### Part 0: Basics
#   Is there a relationship between major type and gender?
#   
#   In tabular form, the data are
#
#   Type    | MNS | HSS | HUM | ART |
#   Female  |  12 |  16 |  19 |   9 | 
#   Male    |   8 |   9 |  13 |   9 | 

# Create the matrix:
data = matrix( c(12,16,19,9, 8,9,13,9), ncol=4, byrow=TRUE)

# Perform the test:
chisq.test(data)

# We did not detect a relationship between gender and major type
# (p-value = 0.8325). We cannot conclude that the major distribution
# differs for the genders.




### Part I: Hair and Eyes
#   Is there a relationship between natural hair color
#   and natural eye color?

dt = read.csv("http://rfs.kvasaheim.com/data/hairandeyecolor.csv")
attach(dt)
summary(dt)

table(eye,hair)

chisq.test( table(eye,hair) )

# We did not detect a relationship between hair color and eye
# color (p-value = 0.2926).

# Graphic

assocplot( table(eye,hair) )
mosaicplot( table(eye,hair) )

detach(dt)




### Part II: Kafka and the Cats
# Can we find some factors that may be related to a person's 
# choice of favorite Murakami book?

# Data exploation

dt = read.csv("http://rfs.kvasaheim.com/data/murakami.csv")
attach(dt)

summary(dt)


## gender?

table(gender,book)
chisq.test( table(gender,book) )

# Yep. It appears as though males prefer 1Q84 to the other
# books and females prefer Kafka on the Shore.


## eye color?

table(eyecolor,book)
chisq.test( table(eyecolor,book) )

# Yep. It appears as though eye color and book are dependent. Brown-
# eyed people do not like the Wind Up Bird Chronicle, but blue-eyed
# people really seem to like it.


## nationality?

table(nationality,book)
chisq.test( table(nationality,book) )

# Yep. It appears as though nationality and book are dependent. Czechs
# seem to really like 1Q84, and so do the Japanese. Americans do not
# seem to like that book.


## vote?

table(vote,book)
chisq.test(table(vote,book))

# Nope. It does not appear as though political vote has anything to do
# with which book is most liked.


### NOTE
# The previous "analysis" is frequently done by business planners. The
# correct next step is to gather additional data and test the hypotheses
# constructed above. The usual next step, however, is to treat these
# provisional conclusions as being Truth.
#
# We were just exploring the data. At no point did we conclude anything
# definitely. 


detach(dt)