[R] two-tailed exact binomail test

[Matthias Kohl]

Peter Dalgaard wrote:

>katrina smith <chezsmithy at yahoo.co.uk> writes:
>
>  
>
>>I am trying to find a definition for the two-tailed exact binomial
>>test but have been unsuccessful. Can you help?
>>    
>>
>
>Just read binom.test. The relevant bit is this:
>(m is the mean == n*p)
>
>            else if (x < m) {
>                i <- seq(from = ceiling(m), to = n)
>                y <- sum(dbinom(i, n, p) <= d * relErr)
>                pbinom(x, n, p) + pbinom(n - y, n, p, lower = FALSE)
>            }
>
>i.e. we take the lower tail, including the value observed + the part
>of the upper tail where the binomial density is less than or equal to
>that of x (with a little fuzz added in). Symmetrically for observations
>in the upper tail of course.
>
>If you were looking for an "official" definition of the two sided
>exact test, I don't think one exists. R's version is equivalent to the
>likelihood ratio test, but there are alternatives (tail-balancing,
>doubling the one-sided p, and maybe more).
>
>  
>
there is a reference:
Section 2.4.2 ("Zweiseitige Tests in einparametrigen 
Exponentialfamilien" - two sided tests in one-parameter exponential 
families) in

H. Witting (1985): Mathematische Statistik I. Teubner. Stuttgart

confer Satz 2.70, Korollar 2.73 (in case of symmetry)
and Beispiel 2.74 (application of Korollar 2.73 to binomial model for p= 
0.5).

Matthias