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The difference between chisq.test binom.test and pbinom
3 messages · Tal Galili, Peter Ehlers
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.Galili at 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]]
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