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 <frien...@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, rip...@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
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