From wdunlap at tibco.com  Wed May  7 22:41:09 2014
From: wdunlap at tibco.com (William Dunlap)
Date: Wed, 7 May 2014 13:41:09 -0700
Subject: [Rd] historical significance of Pr(>Chisq) < 2.2e-16
In-Reply-To: <536A3CE8.2010909@yorku.ca>
References: <536A3CE8.2010909@yorku.ca>
Message-ID: <CAF8bMcZRA=Jo+ozuWBzWLN165GXY93ycXLSYO4ABEAvqaGs_Cw@mail.gmail.com>

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.
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
>>
>
> --
> Michael Friendly     Email: friendly AT yorku DOT ca
> Professor, Psychology Dept. & Chair, Quantitative Methods
> York University      Voice: 416 736-2100 x66249 Fax: 416 736-5814
> 4700 Keele Street    Web:   http://www.datavis.ca
> Toronto, ONT  M3J 1P3 CANADA
>
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[Rd] historical significance of Pr(>Chisq) < 2.2e-16
William Dunlap