Re: [R] two-tailed exact binomail test

From: Matthias Kohl <Matthias.Kohl_at_uni-bayreuth.de>
Date: Sun 28 Aug 2005 - 03:39:42 EST

Peter Dalgaard wrote:

>katrina smith <chezsmithy@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



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