[R] null distribution of binom.test p values

[Greg Snow]

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.snow at imail.org
801.408.8111


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Chris Wallace
> Sent: Thursday, January 26, 2012 5:44 AM
> To: r-help at 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.
> 
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