..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.hard...@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.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. > > ----- ------------------------ 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. ______________________________________________ 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.
