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. ?s 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 >
Sorry, forgot to sign the previous e-mail. Rui Barradas ?s 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. > > ?s 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 >> > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.
Hi,
the lower critical value is zero since:
> cbind(0:2, pbinom(0:2, 26, 0.1))
[,1] [,2]
[1,] 0 0.06461082
[2,] 1 0.25126430
[3,] 2 0.51050524
the upper critical value c_u=6 since:
> cbind(5:7, pbinom((5:7), 26, 0.1))
[,1] [,2]
[1,] 5 0.9601407
[2,] 6 0.9881313
[3,] 7 0.9970172
with F(c_u)>=0.975 and F(c_u-1)<0.975 .
Thus,
* x=6 is in [0,6] => can not reject null
* p-value 0.03985 < 0.05 => reject null
Am 03.04.22 um 20:19 schrieb Rui Barradas:> 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.
>
> ?s 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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