Carl -
Under the null hypothesis, the distribution of p-values for
any statistical test should be uniform over the range from 0 to
1. So while the individual p-values you see in an experiment
like the one you carried out aren't really meaningful, their
ensemble behaviour is. So if you did something like
pvals = replicate(10000,
{randa<-runif(1000);randb<-runif(1000);t.test(randa,randb)$p.value})
ks.test(pvals,'punif')
you'd expect the ks.test to support the hypothesis that the pvals
follow a U(0,1) distribution. As others have pointed out, there are
many other issues regarding random number generation, but I think what
I've described addresses the issue of the t.test probabilities.
- Phil Spector
Statistical Computing Facility
Department of Statistics
UC Berkeley
spec...@stat.berkeley.edu
On Wed, 2 Feb 2011, Carl Witthoft wrote:
Hi, subject more or less says it all.
I freely admit to not having bothered to find some of the online papers about
method of testing the quality of random number generators -- but in an idle
moment I wondered what to expect from something like the following:
randa<-runif(1000)
randb<-runif(1000)
t.test(randa,randb)$p.value
var.test(randa,randb)$p.value
[repeat ad nauseum]
Is the range of p-values I get in any way related tothe "quality" of the
random number generator?
thanks
Carl
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