[R] limit to p-value using t.test()

[Michael Erickson]

On Sat, Feb 6, 2010 at 8:53 AM, Pete Shepard <peter.shepard at gmail.com> wrote:
> I am using t-test to check if the difference between two populations is
> significant. I have a large N=20,000, 10,000 in each population. I compare a
> few different populations with each other and though I get different t-scores,
> I get the same  p-value of 10^-16 which seems like the limit for this
> function. Is this true and is so, is there a workaround to get a more
> sensitive/accurate p-value?

Three comments --

First, with a given value of t and the df for your test, you can get
p-values smaller than  2.2e-16 by plugging that information into pt().

> pt(500, df=10, lower.tail=FALSE)
[1] 1.259769e-23
> pt(1500, df=10, lower.tail=FALSE)
[1] 2.133778e-28

Second, if these are *populations* then a t-test is inappropriate.
Just compute the means, and if they do not equal one another, then the
population means are different.  All the statistical tests that I can
think of try to make and place bounds on inferences about the
population based upon samples drawn from those populations.  If you
have the populations, this makes no sense.  It seems like you need to
decide what kinds of differences are meaningful, and then check to see
if the population differences meet those criteria.

Third, why do you want a more accurate p-value?  The only reason I can
think of is using Rosenthal & Rubin's method to compute effect sizes
from a p-value, but again, if you have the populations, you can
compute effect sizes directly.

Good luck!

Michael