[R] general question on binomial test / sign test

Thu Sep 2 16:24:06 CEST 2010

..i'd like to add that i actually wanted to test the location of differences
of paired samples coming from an non-normal asymetric distribution. the
alternative hypothesis was that negative differences are more often than in
0.5 of all cases. thus i tested
(x=nr.diff.under.0,n=all.diffs,0.5,alternative="greater").
then this one of many tests for a sparse dataset came up where x=0, and
n=1). there i thought the H0 is x is less than 0.5, and i then had my
trouble interpreting the p-value of 1.

best,
kay
Kay Cichini wrote:
> 
> 
> 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.
>>>>>
>>>>> ______________________________________________
>>>>> R-help at r-project.org mailing list
>>>>> 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.
>>>>
>>>>
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> 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.
>>
>> --------------------------------------------------------------------
>> 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
>> ------------------------------ XFMail ------------------------------
>>
>>
> 
> ______________________________________________
> R-help at r-project.org mailing list
> 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.
> 
> 

-----
------------------------
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-tp2419965p2524245.html
Sent from the R help mailing list archive at Nabble.com.