# Handout  for  GLM          by Yu-Ling Tseng
#         Fisher exact test   

# Ex1: Fisher's tea taster, p.46, Table 2.8
> n.table<-array(data = c(3, 1, 1, 3), dim = c(2,2), 
+ dimnames=list(Actual = c("Pour Milk", "Pour Tea"), 
+            Guess = c("Pour Milk", "Pour Tea")))
> n.table
           Guess
Actual      Pour Milk Pour Tea
  Pour Milk         3        1
  Pour Tea          1        3
> 
> 
> #P(3)
> dhyper(3, 4, 4, 4) 
[1] 0.2285714
> 
> #P(0),...,P(4)
> dhyper(0:4, 4, 4, 4)     ## Column 1 of Table 2.9, p. 47
[1] 0.01428571 0.22857143 0.51428571 0.22857143 0.01428571
> 
> 
> fisher.test(x = n.table)

        Fisher's Exact Test for Count Data

data:  n.table 
p-value = 0.4857     ## c.f. Line 1, p. 48
alternative hypothesis: true odds ratio is not equal to 1 
95 percent confidence interval:
   0.2117329 621.9337505   ## c.f. Line -3, p. 48.
sample estimates:
odds ratio 
  6.408309 

> fisher.test(x = n.table, alternative = "greater")

        Fisher's Exact Test for Count Data

data:  n.table 
p-value = 0.2429     ## c.f. Line 9, p. 47.  Note: it= two-sided P-value/2, see Line 13, p. 48
alternative hypothesis: true odds ratio is greater than 1 
95 percent confidence interval:
 0.3135693       Inf 
sample estimates:
odds ratio 
  6.408309 

# EX2: example used in class
> n.table<-array(data = c(2, 1, 3, 1), dim = c(2,2), 
+  dimnames=list(Actual = c("Pour Milk", "Pour Tea"), 
+            Guess = c("Pour Milk", "Pour Tea")))
> n.table
           Guess
Actual      Pour Milk Pour Tea
  Pour Milk         2        3
  Pour Tea          1        1
> 
> 
> 
> 
> #P(1),...,P(3)
> dhyper(1:3, 3, 4, 5) 
[1] 0.1428571 0.5714286 0.2857143
> 
> 
> fisher.test(x = n.table)

        Fisher's Exact Test for Count Data

data:  n.table 
p-value = 1
alternative hypothesis: true odds ratio is not equal to 1 
95 percent confidence interval:
  0.006400778 78.183984029 
sample estimates:
odds ratio 
 0.7071212 

> fisher.test(x = n.table, alternative = "greater")

        Fisher's Exact Test for Count Data

data:  n.table 
p-value = 0.8571
alternative hypothesis: true odds ratio is greater than 1 
95 percent confidence interval:
 0.01307242        Inf 
sample estimates:
odds ratio 
 0.7071212 

> 
> # Create a cross-classified table out of Table 2.10
> vic.race<-c("white","black")
> def.race<-vic.race
> death.penalty<-c("yes", "no")
> datalabel<-list(defendant=def.race,death=death.penalty,victim=vic.race)
> table.2.6<- expand.grid(defendant=def.race,death=death.penalty,victim=vic.race) 
> Data<-c(53, 11, 414, 37, 0, 4, 16, 139)
> table.2.6<-cbind(table.2.6,count=Data)
> table.2.6
  defendant death victim count
1     white   yes  white    53
2     black   yes  white    11
3     white    no  white   414
4     black    no  white    37
5     white   yes  black     0
6     black   yes  black     4
7     white    no  black    16
8     black    no  black   139

> temp<-xtabs(count~defendant+death+victim ,data=table.2.6)
> temp
, , victim = white

         death
defendant yes  no
    white  53 414
    black  11  37

, , victim = black

         death
defendant yes  no
    white   0  16
    black   4 139