# Edps/Psych/Soc 584
# Fall 2018
# C.J.Anderson
#
#  UofI Admissions Scandel (2 x 2 table)
#  The data were from White's e-mail.
#
#   Part of the argument that White made was that the general admission rate was 69% and 
#   the rate on the I List was higher but it only lead to only additional 13 students being
#   admitted.  
#
#   160 students on the I list
#   123 admitted
#   76.88% admitted from I list
#
#   69% of 160 = 110.... so 123 - 110 = 13  (i.e., number admitted from I list minus 69% is 13)
#

library(Epi)                # for twoby2
library(MASS)               # for loglm
library(vcd)                # for assocstats

# create data frame
var.levels <- expand.grid(admit=c("yes","no"), Ilist=c("Ilist","General"))
( scandel <- data.frame(var.levels, count=c(123, 37, 18000 , 8000) ) )

# tabular form
scandel.tab <- xtabs(count ~ admit + Ilist, data=scandel)
addmargins(scandel.tab)

# data should be in matrix form -- this keeps row & column names and level values
( scandel.mat <- as.matrix(scandel.tab) )

# Compute differences, relative risk & odds ratio, including CIs
twoby2(scandel.mat)


# Chi-square test statistics:   data frame (case data)
loglm(count ~ admit + Ilist, data=scandel)

# or --- this includes Yate's correction for continuity, which isn't used much anymore
chisq.test(scandel.tab) 

# or 
ax <- as.factor(scandel$admit)
ix <- as.factor(scandel$Ilist)
glm(count ~ ax + ix, data=scandel, family=poisson)

# or 
assocstats(scandel.tab)