[R] exact values for p-values - more information.

[Spencer Graves]

	  I just checked:

 > pf(39540, 1, 7025, lower.tail=FALSE, log.p=TRUE)
[1] -Inf

	  This is not correct.  With 7025 denominator degrees of freedom, we 
might use the chi-square approximation to the F distribution:
	
 > pchisq(39540, 1, lower.tail=FALSE, log.p=TRUE)
[1] -19775.52

	  In sum, my best approximation to  pf(39540, 1, 7025, 
lower.tail=FALSE, log.p=TRUE), given only a minute to work on this, is 
exp(pchisq(39540, 1, lower.tail=FALSE, log.p=TRUE)) = exp(-19775.52).

	  I'm confident that many violations of assumptions would likely be 
more important than the differences between "p-value: < 2.2e-16" and 
these other two answers.  However, I have also used numbers like 
exp(-19775.52) to guestimate relative degrees of plausibility for 
different alternatives.  That doesn't mean they are right, only the best 
I can get with the available resources.

	  spencer graves

Achim Zeileis wrote:

> On Mon, 11 Jul 2005, S.O. Nyangoma wrote:
> 
> 
>> Hi there,
>> If I do an lm, I get p-vlues as
>>
>> p-value: < 2.2e-16
>>
>>This is obtained from F =39540 with df1 = 1, df2 = 7025.
>>
>> Suppose am interested in exact value such as
>>
>> p-value = 1.6e-16 (note = and not <)
>>
>> How do I go about it?
> 
> 
> You can always extract the `exact' p-value from the "summary.lm" object or
> you can compute it by hand via
>   pf(39540, df1 = 1, df2 = 7025, lower.tail = FALSE)
> For all practical purposes, the above means that the p-value is 0.
> I guess you are on a 32-bit machine, then it also means that the p-value
> is smaller than the Machine epsilon
>   .Machine$double.eps
> 
> So if you want to report the p-value somewhere, I think R's output should
> be more than precise enough. If you want to compute some other values that
> depend on such a p-value, then it is probably wiser to compute on a log
> scale, i.e. instead
>   pf(70, df1 = 1, df2 = 7025, lower.tail = FALSE)
> use
>   pf(70, df1 = 1, df2 = 7025, lower.tail = FALSE, log.p = TRUE)
> 
> However, don't expect to be able to evaluate it at such extreme values
> such as 39540.
> Z
> 
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Spencer Graves, PhD
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