Hi guys,

I want to use fisher.test() to perform association analysis but I meet a confused problem.

In a test data, different "alternative" will derive to different pValue

> fisher.test(c(1,0,1,0,0,0,1,1,1,1,1,1),c(1,0,1,1,1,1,0,0,1,0,0,0))

    Fisher's Exact Test for Count Data

data:  c(1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1) and c(1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0)
p-value = 0.5455
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.00319446 4.50042353
sample estimates:
odds ratio 
  0.230358 

> fisher.test(c(1,0,1,0,0,0,1,1,1,1,1,1),c(1,0,1,1,1,1,0,0,1,0,0,0),alternative = "less")

    Fisher's Exact Test for Count Data

data:  c(1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1) and c(1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0)
p-value = 0.2727
alternative hypothesis: true odds ratio is less than 1
95 percent confidence interval:
 0.000000 3.151343
sample estimates:
odds ratio 
  0.230358

But in a larger data which is also binary entries with 0 and 1, the pValue is perfectly the same! Why?

> as.numeric(x)
  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0
 [55] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
[109] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[163] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[217] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
> as.numeric(y)
  [1] 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1
 [55] 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0
[109] 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1
[163] 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1
[217] 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1
> fisher.test(as.numeric(x),as.numeric(y),alternative = "two.side")

    Fisher's Exact Test for Count Data

data:  as.numeric(x) and as.numeric(y)
p-value = 0.0002977
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.001366782 0.412310161
sample estimates:
odds ratio 
0.05916957 

> fisher.test(as.numeric(x),as.numeric(y),alternative = "less")

    Fisher's Exact Test for Count Data

data:  as.numeric(x) and as.numeric(y)
p-value = 0.0002977
alternative hypothesis: true odds ratio is less than 1
95 percent confidence interval:
 0.000000 0.337174
sample estimates:
odds ratio 
0.05916957

Hope somebody could give this an explaination. Thx a lot!