From: Matthias Kohl <Matthias.Kohl_at_uni-bayreuth.de>

Date: Sun 28 Aug 2005 - 03:39:42 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Aug 28 03:48:53 2005

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

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Aug 28 03:48:53 2005

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