[Rd] historical significance of Pr(>Chisq) < 2.2e-16
Prof Brian Ripley
ripley at stats.ox.ac.uk
Thu May 8 08:38:57 CEST 2014
On 07/05/2014 21:41, William Dunlap wrote:
> It may come a time before the pchisq() function had the lower.tail
> argument. In those days you had the compute the upper tail as
> 1-pchisq(x2, df). For any eps<2.2e-16 (.Machine$double.eps), 1-eps==1
> so 1-(1-eps)==0 so you would get, e.g.,
> > 1-pchisq(100,2)
> [1] 0
> and people would say 'but the p-value is not 0: it may be very small
> but not zero' so anova's printing functions would say "<2.2e-16" to
> mollify them.
>
> Now we have the lower.tail=FALSE argument
> > pchisq(100,2,lower.tail=FALSE)
> [1] 1.92875e-22
> and don't need the "<2.2e-16" but no one has seen fit to change things.
Because although pchisq has that argument, not all pxxx functions
guarantee accuracy in the upper tail (and might compute 1-p internally).
And the print() method for class "anova" has no idea how the p values
supplied were computed (as below, they could have been done by
third-party code).
Only in very unusual circumstances does it matter how small a p-value
less than, say, 1e-6 is. For many cases (including anova) the computed
value depends on fine details of the null hypothesis which are
implausible, so a secondary effect is to avoid drawing attention to
numbers which should be taken only as a very rough guide.
> Bill Dunlap
> TIBCO Software
> wdunlap tibco.com
>
>
> On Wed, May 7, 2014 at 7:02 AM, Michael Friendly <friendly at yorku.ca> wrote:
>> Where does the value 2.2e-16 come from in p-values for chisq tests such as
>> those
>> reported below?
>>
>>> Anova(cm.mod2)
>> Analysis of Deviance Table (Type II tests)
>>
>> Response: Freq
>> LR Chisq Df Pr(>Chisq)
>> B 11026.2 1 < 2.2e-16 ***
>> W 7037.5 1 < 2.2e-16 ***
>> Age 886.6 8 < 2.2e-16 ***
>> B:W 3025.2 1 < 2.2e-16 ***
>> B:Age 1130.4 8 < 2.2e-16 ***
>> W:Age 332.9 8 < 2.2e-16 ***
>> ---
>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
More information about the R-devel
mailing list