[R] general question on binomial test / sign test

Kay Cecil Cichini Kay.Cichini at uibk.ac.at
Thu Sep 2 14:39:38 CEST 2010 

thanks a lot for the elaborations.

your explanations clearly brought to me that either  
binom.test(1,1,0.5,"two-sided") or binom.test(0,1,0.5) giving a  
p-value of 1 simply indicate i have abolutely no ensurance to reject H0.

considering binom.test(0,1,0.5,alternative="greater") and  
binom.test(1,1,0.5,alternative="less") where i get a p-value of 1 and  
0.5,respectively - am i right in stating that for the first estimate  
0/1 i have no ensurance at all for rejection of H0 and for the second  
estimate = 1/1 i have same chance for beeing wrong in either rejecting  
or keeping H0.

many thanks,
kay



Zitat von Ted.Harding at manchester.ac.uk:

> You state: "in reverse the p-value of 1 says that i can 100% sure
> that the estimate of 0.5 is true". This is where your logic about
> significance tests goes wrong.
>
> The general logic of a singificance test is that a test statistic
> (say T) is chosen such that large values represent a discrepancy
> between possible data and the hypothesis under test. When you
> have the data, T evaluates to a value (say t0). The null hypothesis
> (NH) implies a distribution for the statistic T if the NH is true.
>
> Then the value of Prob(T >= t0 | NH) can be calculated. If this is
> small, then the probability of obtaining data at least as discrepant
> as the data you did obtain is small; if sufficiently small, then
> the conjunction of NH and your data (as assessed by the statistic T)
> is so unlikely that you can decide to not believe that it is possible.
> If you so decide, then you reject the NH because the data are so
> discrepant that you can't believe it!
>
> This is on the same lines as the "reductio ad absurdum" in classical
> logic: "An hypothesis A implies that an outcome B must occur. But I
> have observed that B did not occur. Therefore A cannot be true."
>
> But it does not follow that, if you observe that B did occur
> (which is *consistent* with A), then A must be true. A could be
> false, yet B still occur -- the only basis on which occurrence
> of B could *prove* that A must be true is when you have the prior
> information that B will occur *if and only if* A is true. In the
> reductio ad absurdum, and in the parallel logic of significance
> testing, all you have is "B will occur *if* A is true". The "only if"
> part is not there. So you cannot deduce that "A is true" from
> the observation that "B occurred", since what you have to start with
> allows B to occur if A is false (i.e. "B will occur *if* A is true"
> says nothing about what may or may not happen if A is false).
>
> So, in your single toss of a coin, it is true that "I will observe
> either 'succ' or 'fail' if the coin is fair". But (as in the above)
> you cannot deduce that "the coin is fair" if you observe either
> 'succ' or 'fail', since it is possible (indeed necessary) that you
> obtain such an observation if the coin is not fair (even if the
> coin is the same, either 'succ' or 'fail', on both sides, therefore
> completely unfair). This is an attempt to expand Greg Snow's reply!
>
> Your 2-sided test takes the form T=1 if either outcome='succ' or
> outcome='fail'. And that is the only possible value for T since
> no other outcome is possible. Hence Prob(T==1) = 1 whether the coin
> is fair or not. It is not possible for such data to discriminate
> between a fair and an unfair coin.
>
> And, as explained above, a P-value of 1 cannot prove that the
> null hypothesis is true. All that is possible with a significance
> test is that a small P-value can be taken as evidence that the
> NH is false.
>
> Hoping this helps!
> Ted.
>
> On 02-Sep-10 07:41:17, Kay Cecil Cichini wrote:
>> i test the null that the coin is fair (p(succ) = p(fail) = 0.5) with
>> one trail and get a p-value of 1. actually i want to proof the
>> alternative H that the estimate is different from 0.5, what certainly
>> can not be aproven here. but in reverse the p-value of 1 says that i
>> can 100% sure that the estimate of 0.5 is true (??) - that's the point
>> that astonishes me.
>>
>> thanks if anybody could clarify this for me,
>> kay
>>
>> Zitat von Greg Snow <Greg.Snow at imail.org>:
>>
>>> Try thinking this one through from first principles, you are
>>> essentially saying that your null hypothesis is that you are
>>> flipping a fair coin and you want to do a 2-tailed test.  You then
>>> flip the coin exactly once, what do you expect to happen?  The
>>> p-value of 1 just means that what you saw was perfectly consistent
>>> with what is predicted to happen flipping a single time.
>>>
>>> Does that help?
>>>
>>> If not, please explain what you mean a little better.
>>>
>>> --
>>> Gregory (Greg) L. Snow Ph.D.
>>> Statistical Data Center
>>> Intermountain Healthcare
>>> greg.snow at imail.org
>>> 801.408.8111
>>>
>>>
>>>> -----Original Message-----
>>>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
>>>> project.org] On Behalf Of Kay Cichini
>>>> Sent: Wednesday, September 01, 2010 3:06 PM
>>>> To: r-help at r-project.org
>>>> Subject: [R] general question on binomial test / sign test
>>>>
>>>>
>>>> hello,
>>>>
>>>> i did several binomial tests and noticed for one sparse dataset that
>>>> binom.test(1,1,0.5) gives a p-value of 1 for the null, what i can't
>>>> quite
>>>> grasp. that would say that the a prob of 1/2 has p-value of 0 ?? - i
>>>> must be
>>>> wrong but can't figure out the right interpretation..
>>>>
>>>> best,
>>>> kay
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> -----
>>>> ------------------------
>>>> Kay Cichini
>>>> Postgraduate student
>>>> Institute of Botany
>>>> Univ. of Innsbruck
>>>> ------------------------
>>>>
>>>> --
>>>> View this message in context: http://r.789695.n4.nabble.com/general-
>>>> question-on-binomial-test-sign-test-tp2419965p2419965.html
>>>> Sent from the R help mailing list archive at Nabble.com.
>>>>
>>>> ______________________________________________
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>>>> PLEASE do read the posting guide http://www.R-project.org/posting-
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>>>
>>>
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
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>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 02-Sep-10                                       Time: 09:42:34
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