Dear Peter, Your explanation makes perfect sense, thank you.
With regards, Tal ----------------Contact Details:------------------------------------------------------- Contact me: tal.gal...@gmail.com | 972-52-7275845 Read me: www.talgalili.com (Hebrew) | www.biostatistics.co.il (Hebrew) | www.r-statistics.com (English) ---------------------------------------------------------------------------------------------- On Tue, Aug 21, 2012 at 2:08 AM, Peter Ehlers <ehl...@ucalgary.ca> wrote: > On 2012-08-20 12:24, Tal Galili wrote: > >> Hello all, >> I am trying to understand the different results I am getting from the >> following 3 commands: >> >> chisq.test(c(62,50), p = c(0.512,1-0.512), correct = F) # p-value = 0.3788 >> binom.test(x=62,n=112, p= 0.512) # p-value = 0.3961 >> 2*(1-pbinom(62,112, .512)) # p-value = 0.329 >> >> Well, the binom.test was supposed to be "exact" and give the same results >> as the pbinom, while the chisq.test relies on the normal asymptotics. So >> I >> would imagine the binom.test should be equal to one of the other two >> lines, >> but it is not. >> >> The same happens for larger numbers as well: >> >> chisq.test(c(1395,1278), p = c(0.512,1-0.512), correct = F) >> # chisq.test(c(1395,1278), p = c(0.512,1-0.512), simulate.p.value= T) >> binom.test(x=1395,n=2673, p= 0.512) >> 2*(1-pbinom(1395,2673, .512)) >> > > Let's first dispense with the chisq.test value; that uses the Normal > approximation and the calculation is trivial; the other two don't. > > Let's do a one-sided test: > > binom.test(x=62, n=112, p=.512, alternative="greater")$p.value > # 0.2161936 > > Compare with: > > pbinom(61, 112, .512, lower.tail=FALSE) > # 0.2161936 > > Why '61' instead of '62'? Because we want to include 62 in the > upper tail probability. > > Now it's just a matter of how to calculate the lower tail probability > in binom.test. Hint: it's not just set equal to the upper tail > probability (hence no '2*xxx'). > The expected value (under H0) is 112*0.51 = 57.12. > Thus 62 is 4.88 ~ 5 units higher than the EV. > Now calculate the probability of an outcome that is 5 units *less* > (or lower) than the EV: > > pbinom(52, 112, .512) > # 0.1799121 > > Add the two probabilities to get: > > 0.2161936 + 0.1799121 > # 0.3961057 > > and that's what binom.test() reports. > For details, have a look at the binom.test code. > > Peter Ehlers > > >> >> I'd be happy to know what I might be missing. >> >> Thanks, >> Tal >> >> >> ----------------Contact >> Details:----------------------**------------------------------**--- >> Contact me: tal.gal...@gmail.com | 972-52-7275845 >> Read me: www.talgalili.com (Hebrew) | www.biostatistics.co.il (Hebrew) | >> www.r-statistics.com (English) >> ------------------------------**------------------------------** >> ------------------------------**---- >> >> [[alternative HTML version deleted]] >> >> ______________________________**________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/**listinfo/r-help<https://stat.ethz.ch/mailman/listinfo/r-help> >> PLEASE do read the posting guide http://www.R-project.org/** >> posting-guide.html <http://www.R-project.org/posting-guide.html> >> and provide commented, minimal, self-contained, reproducible code. >> >> > [[alternative HTML version deleted]] ______________________________________________ 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.
