# Math 322 Biostatistics
# Lecture, March 18, 2009
# R examples for Chapter 10.1-2 (2x2 Contingency tables)
# Geir Arne Hjelle (hjelle@math.wustl.edu)

# Consider the example from the lecture looking at the relationship
# between gender and handedness
#
#               | Boys       Girls    |   Total
# --------------+---------------------+---------
# Left-handed   |   6          12     |     18
# Right-handed  |  28          24     |     52
# --------------+---------------------+---------
# Total         |  34          36     |     70
#
# To use R to test for whether the proportion of left-handed boys is
# equal to the proportion of left-handed girls, we can use chisq.test().
#
# First construct a 2x2 matrix with the observed data
observed <- matrix( c(6, 28, 12, 24), ncol = 2 )

# Then test the data
chisq.test(observed)

# We can also perform the test without the continuity correction
# (see the paragraph at the bottom of page 398 and top of page 399
#  in the book for a discussion about the Yates correction).
chisq.test(observed, correct = FALSE)

# If the data are given to us in a "full format", we can either use table
# to make a summary, or use chisq.test() directly on the data.
#
# Assume we have two paired vectors with all 70 observations above.
gender <- rep(c("Boy", "Girl"), c(34, 36))
handedness <- rep(c("Left", "Right", "Left", "Right"), c(6, 28, 12, 24))
data <- data.frame(gender, handedness)

# Using table to make a frequency matrix
table(data)
chisq.test(table(data))

# Sending the vectors directly to chisq.test()
chisq.test(gender, handedness)

# As a final remark, note that because of the symmetry of the problem and
# of the calculations, it does not matter which vector we specify first,
# and which we specify second.
chisq.test(handedness, gender)

# Similarly, we can transpose the 2x2 contingency table (matrix) and
# still get the same results
t(observed)
chisq.test(t(observed))