[R] binom.test()

[Thomas Lumley]

On Mon, 23 Sep 2002, Robin Hankin wrote:

> Hello everybody.
>
> Does anyone else find the last test in the following sequence odd?
> Can anyone else reproduce it or is it just me?
>
>
> > binom.test(100,200,0.13)$p.value
> [1] 2.357325e-36
> > binom.test(100,200,0.013)$p.value
> [1] 6.146546e-131
> > binom.test(100,200,0.0013)$p.value
> [1] 1.973702e-230
> > binom.test(100,200,0.00013)$p.value
> [1] 0.9743334
>

Yes. The p-value is evaluated by adding up binomial probabilities, but it
leads to catastrophic rounding error.

One solution would be to use the incomplete beta function (pbeta) either
always or in extreme cases.  That's how the confidence limits are computed
and they don't break down in this case.

So eg
> pbeta(0.13,100,101)
[1] 2.357325e-36
> pbeta(0.013, 100, 101)
[1] 6.146546e-131
> pbeta(0.0013,100,101)
[1] 1.973702e-230
> pbeta(0.00013, 100, 101)
[1] 0
which agrees on the first three and is a lot closer on the last.


	-thomas

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