# [R] binom.test & p-value

Rui Barradas ru|pb@rr@d@@ @end|ng |rom @@po@pt
Sun Apr 3 20:21:15 CEST 2022

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Às 19:19 de 03/04/2022, Rui Barradas escreveu:
> Hello,
>
> Can you post your computations? Assuming a two-sided test, mine are
>
>
> x <- 6
> n <- 26
> p <- 0.1
>
> cmb <- sapply(x:n, \(i) choose(n, i))
> sum(cmb * p^(x:n) * (1 - p)^(n - (x:n)))
> #[1] 0.03985931
>
> binom.test(x=6, n=26, p=0.1)\$p.value
> #[1] 0.03985931
>
>
> The result are equal to one another.
>
> Às 19:00 de 03/04/2022, Sigbert Klinke escreveu:
>> Hi,
>>
>> for the specific example binom.test(x=6, n=26, p=0.1) I get as p-value
>> 0.03986. The default approach to decide whether I can reject the null
>> or or not is to compare the p-value with the given significance level.
>> Using a significance level of 0.05 this will lead to reject the null
>> hypothesis.
>>
>> However, computing things by hand it turned out that the critical
>> values are 0 and 6. Since the test statistic is also 6 I can not
>> reject the null hypothesis.
>>
>> I found the discussion under
>> https://stat.ethz.ch/pipermail/r-help/2009-February/380341.html and I
>> understand that a p-value is not well defined if we have a asymmmetric
>> (discrete) distribution under the null.
>>
>> At least I would have expected some hint in the documentation for
>> binom.test.
>>
>> Sigbert
>>
>
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