[R] Incorrect p value for binom.test?

Peter Dalgaard p.dalgaard at biostat.ku.dk
Thu Feb 5 21:48:11 CET 2009

```Michael Grant wrote:
> I believe the binom.test procedure is producing one tailed p values
> rather than the two tailed value implied by the alternative hypothesis
> language.  A textbook and SAS both show 2*9.94e-07 = 1.988e-06 as the
> two tailed value.  As does the R summation syntax from R below.  It
> looks to me like the alternative hypothesis language should be revised
> to something like " ... greater than or equal to ..."  Am I mistaken?

Yes. Or maybe, it is a matter of definition. The problem is that

> (0:25)[dbinom(0:25,25,.061) <= dbinom(10,25,.061)]
[1] 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

so with R's definition of "more extreme", all such values are in the
upper tail.

Actually, if you look at the actual distribution, I think you'll agree
that it is rather difficult to define a lower tail with positive
probability that corresponds to X >= 10.

> round(dbinom(0:25,25,.061),6)
[1] 0.207319 0.336701 0.262476 0.130726 0.046708 0.012744
[7] 0.002760 0.000487 0.000071 0.000009 0.000001 0.000000
[13] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
[19] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
[25] 0.000000 0.000000

In any case, you would be hard pressed to find a subset of 0:25 that has
the probability that SAS and your textbook claims as the p value.

>
>
>
> M.C.Grant
>
>
>
>> 2*sum(dbinom(c(10:25),25,0.061))
>
> [1] 1.987976e-06
>
>
>
>> binom.test(10,25,0.061)
>
>
>
>         Exact binomial test
>
>
>
> data:  10 and 25
>
> number of successes = 10, number of trials = 25, p-value = 9.94e-07
>
> alternative hypothesis: true probability of success is not equal to
> 0.061
>
> 95 percent confidence interval:
>
>  0.2112548 0.6133465
>
> sample estimates:
>
> probability of success
>
>                    0.4
>
>
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>
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