> On 14 Dec 2014, at 13:54 , Stefan Evert <stefa...@collocations.de> wrote: > <snip> > >> (3) What is people's view on computing the two-tailed test like this, >> which leads to an ns result unlike binom.test? >> 2*sum(dbinom(51:235, 235, 1/6)) # 0.05308849 > > This is a popular approximation (which I also use most of the time) because > it's much less expensive (in computational terms) than computing an exact > (likelihood-based) two-tailed p-value as binom.test() does. This is > particularly relevant if you want to compute confidence intervals for the > true probability p based on a large sample, which takes ages with > binom.test().
When I get drilled about this, I usually say that one really shouldn't use "two-tailed" and "exact" in the same sentence, because of the issue with the definition of tails. I don't agree that the version in binom.test is in any sense _the_ correct one and we probably should make alternatives optional at some point. One point that is easily overlooked (guilty!) is that defining the p-value as the sum over less probable outcomes is _not_ a likelihood theory technique. The likelihood ratio test should have a denominator equal to the maximum probability of the outcome when the parameter is allowed to vary from the null value. It is not that hard to do the actual LRT: > LRT <- -2*log(dbinom(0:235,235,1/6)/dbinom(0:235,235,(0:235)/235)) > dist_null <- dbinom(0:235, 235, 1/6) > sum(dist_null[LRT >= LRT_obs]) [1] 0.05373588 I believe there are four reasonable contenders for the two sided p-value: 1) sum of probabilities of less or equally probable outcomes 2) sum of probabilities of outcomes with more extreme LRT 3) double minimum one-tailed p 4) tail-balancing: one-sided p plus the max opposite tail probability less than p -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@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.
