two-tailed exact binomail test

You might find the answer in Chapter 2 of Nonparametric statistical
methods written by Myles Hollander and Douglas A. Wolfe (2nd ed.,
ISBN: 0-471-19045-4)

2005/8/27, katrina smith <chezsmithy at yahoo.co.uk>:

I am trying to find a definition for the two-tailed exact binomial test but have been unsuccessful. Can you help?




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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).

O__  ---- Peter Dalgaard             ??ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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