# [R] small bug in binom.test?

ripley@stats.ox.ac.uk ripley at stats.ox.ac.uk
Wed Jan 22 09:46:02 CET 2003

```Why do you think that?

The problems binom.test(49,50,0.5) and binom.test(51,100,0.5) are
symmetrical, so one would expect the same results for a two-sided test.

The problem I guess is how a two-sided test is defined for a discrete
distribution.  For one-sided tests one would use the probability of X >=11
or X <= 9, and those are not equal.  For a two-sided test the code
attempts to find a point in the opposite tail with at least as large a
tail probability, and adds on that tail probability.  Thus for
binom.test(11,100,p=0.1) it used P(X < 9 || X >= 11), and for
binom.test(9,100,p=0.1) it used P(X <= 9 || X > 10), if I followed the
code right.

The great thing about R is that you can do

debug(binom.test)

On Wed, 22 Jan 2003, Jerome Goudet wrote:

> Hi all,
>
> I am wondering whether there is a small bug in the binom.test function of
> the ctest library (I'm using R 1.6.0 on windows 2000, but Splus 2000 seems
> to have the same behaviour). Or perhaps I've misunderstood something.
>
> the command binom.test(11,100,p=0.1) and binom.test(9,100,p=0.1) give
> different p-values (see below).  As 9 and 11 are equidistant from 10, the
> mean of the distribution, I would have thought that the probabilities
> should be the same. For instance, binom.test(49,50,0.5) and
> binom.test(51,100,0.5) do give the same results. Any help wouldbe
> appreciated. Jerome
>
>
>
>  > binom.test(11,100,0.1)
>
>          Exact binomial test
>
> data:  11 and 100
> number of successes = 11, number of trials = 100, p-value = 0.7377
> alternative hypothesis: true probability of success is not equal to 0.1
> 95 percent confidence interval:
>   0.05620702 0.18830113
> sample estimates:
> probability of success
>                    0.11
>
>  > binom.test(9,100,0.1)
>
>          Exact binomial test
>
> data:  9 and 100
> number of successes = 9, number of trials = 100, p-value = 0.8681
> alternative hypothesis: true probability of success is not equal to 0.1
> 95 percent confidence interval:
>   0.04198360 0.16398226
> sample estimates:
> probability of success
>                    0.09
>
>
> Jerome GOUDET
> Institut d'Ecologie, Bat. Biologie
> Uni. Lausanne , CH-1015 Lausanne
> Switzerland
> Tel: +41 21 692 42 42    Fax: +41 21 692 42 65
> Secr:+41 21 692 42 60
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-help
>

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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