Re: [R] shapiro wilk normality test

From: Ted Harding <Ted.Harding_at_manchester.ac.uk>
Date: Sun, 13 Jul 2008 21:59:21 +0100 (BST)


On 13-Jul-08 19:53:47, Johannes Huesing wrote:
> Frank E Harrell Jr <f.harrell@vanderbilt.edu> [Sun, Jul 13, 2008 at
> 08:07:37PM CEST]:

>> (Ted Harding) wrote:
>>> On 13-Jul-08 13:29:13, Frank E Harrell Jr wrote:
>>>> [...]
>>>> A large P-value means nothing more than needing more data.  No  
>>>> conclusion is possible.  Please read the classic paper Absence of  
>>>> Evidence is not Evidence for Absence.
>>>

> [...]
>>
>> It's real.  Full text is available to all:  
>> http://www.bmj.com/cgi/content/full/311/7003/485

>
> The quotation is attributed to the late Carl Sagan who
> seemed to have used it as a strawman argument , see
> http://oyhus.no/AbsenceOfEvidence.html.

This citation of Sagan, and the link therein to Sagan quotes:

  http://en.wikiquote.org/wiki/Carl_Sagan

are interesting, as far as they go. However, I disagree with the proof ("by conditional probability") that absence of evidence is evidence of absence.

Definition 1 is disputable. But, whether one agrees with it or not, Definition 2 does not correspond to my interpretation of "absence of evidence". If A is evidence for B (in terms of P(B|A) etc.), this means that if we *know* that A is the case, or that not-A is the case, then we can say something about P(B). But "absence of evidence", in my interpretation (which I believe is right for the statistical context of "non-significant P-values"), means that we do not know about A: we do not have enough information.

That proof needs to be discussed in terms of the available evidence for A!

The proof is, basically, given in terms of a 2-valued logic where every term is either TRUE or FALSE. In the real world we have at least a third possible value: UNKNOWN (or, as R would put it, NA).

Even if you accept (Definition 1) that

  "A is evidence for B" == P(B|A) > P(B|not-A)

what can you possibly say about P(B|NA) (other than that it is NA itself)?

Best wishes to all,
Ted.



E-Mail: (Ted Harding) <Ted.Harding_at_manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 13-Jul-08                                       Time: 21:59:16
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