[R] two-tailed exact binomail test

[Peter Dalgaard]

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).

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