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.s...@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.s...@imail.org >> 801.408.8111 >> >> >>> -----Original Message----- >>> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r- >>> project.org] On Behalf Of Kay Cichini >>> Sent: Wednesday, September 01, 2010 3:06 PM >>> To: r-help@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@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@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.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 02-Sep-10 Time: 09:42:34 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@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.