# 3-way table:  age x smoking x breathing test result
# Edps 589
# Fall 2018
# C.J.Anderson
#

library(vcd)
library(vcdExtra)
library(MASS)
library(DescTools)

var.values <- expand.grid(test=c("normal","not normal"),
                          smoke=c("never","current"),
			              age=c("<40","40-59"))
counts <- c(577, 34, 682, 57, 164, 4, 245, 74)	
ast <- cbind(var.values,counts)
ast


# 2-way marginal table
test.by.smoke<- xtabs(counts ~ test+smoke,data=ast) 
addmargins(test.by.smoke)

# 2-way marginal analysis:  
assocstats(test.by.smoke)             # Compute G2 and X2
( OR <- oddsratio(test.by.smoke)  )   # Compute odds ratio and view
summary(OR)                           # signficant test for odds ratio -- don't really 
                                      #   need because have X2 and G2 from assocstats()
exp(1.013658)					      # odds ratio	 
exp(confint(OR) )                     # Confidnece interval of odds ratio




# 3-way  Table of data
#  -- partial or conditional tables
ast.tab <- xtabs(counts ~ test+smoke+age,data=ast)
addmargins(ast.tab)

# 3-way contitional/partial table analysis 
assocstats(ast.tab)                    # Compute X2 and G2
( OR <- oddsratio(ast.tab)  )          # Compute odds ratio & view
logodds <- summary(OR)                 # Signficant test for odds ratios
exp(logodds[1:3]  )                    # Odds ratios
exp( confint(OR) )                     # Confidnece interval of odds ratios

# First: Test for homogenity (shouldn't be significant...p should = small
WoolfTest(ast.tab)