I believe that what you are seeing is due to the discrete nature of the binomial test. When I run your code below I see the bar between 0.9 and 1.0 is about twice as tall as the bar between 0.0 and 0.1, but the bar between 0.8 and 0.9 is not there (height 0), if you average the top 2 bars (0.8-0.9 and 0.9-1.0) then the average height is similar to that of the lowest bar. The bar between 0.5 and 0.6 is also 0, if you average that one with the next 2 (0.6-0.7 and 0.7-0.8) then they are also similar to the bars near 0.
-- 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-bounces@r- > project.org] On Behalf Of Chris Wallace > Sent: Thursday, January 26, 2012 5:44 AM > To: r-help@r-project.org > Subject: [R] null distribution of binom.test p values > > Dear R-help, > > I must be missing something very obvious, but I am confused as to why > the null distribution for p values generated by binom.test() appears to > be non-uniform. The histogram generated below has a trend towards > values closer to 1 than 0. I expected it to be flat. > > hist(sapply(1:1000, function(i,n=100) > binom.test(sum(rnorm(n)>0),n,p=0.5,alternative="two")$p.value)) > > This trend is more pronounced for small n, and the distribution appears > uniform for larger n, say n=1000. I had expected the distribution to > be > discrete for small n, but not skewed. Can anyone explain why? > > Many thanks, > > Chris. > > ______________________________________________ > 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.
