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st: Re: st: RE: Fisher´s exact test for rxc [2X2] tables: one-tailed or two-tailed[iso-8859-1] ?


From   sjsamuels@gmail.com
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: st: RE: Fisher´s exact test for rxc [2X2] tables: one-tailed or two-tailed[iso-8859-1] ?
Date   Sat, 2 May 2009 10:47:23 -0400

I'm going to retract my previous statement and agree with the Stata
manual that the chi square and exact RxC tests for independence
reported in Stata are properly called  one-sided.

 I'll again use the analogy of the chi square Test, because I believe
that at least one version of the exact test ranks tables on the value
of their chi square statistic.  The chi square test is a test of fit
of the model of independence, and rejects if the chi square statistic
is "too big". Call this a "right-tail" test. The implicit parameter
here is the sum of squares in which counts are replaced by
probabilities.

However one can conceive of a test of  independence, in which the
alternative is 'too good a fit".  For example, RA Fisher believed that
some of Gregory Mendel's observations were too close to expectation to
have occurred by chance.  (For a revisionist view see: CE Novitski
(2004) Revision of Fisher's Analysis of Mendel's Garden Pea
Experiments. Genetics 166: 1139-1140
http://www.genetics.org/cgi/content/full/166/3/1139 ).

If one conducted a test with this alternative, it would reject if the
Chi Square statistic is "too small".  The analogous exact test would
do the same.  This would be a "left-tail" test.

The chi square and exact tests for independence reported by Stata are
indeed  the right-tail tests  and so are "one-sided".

I apologize to Tiago for  my misleading comments.

-Steve

 On Behalf Of Tiago V. Pereira
>> Sent: Friday, May 01, 2009 5:39 AM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: st: [iso-8859-1] Fisher´s exact test for rxc tables: one-tailed or
>> two-ta iled[iso-8859-1] ?
>>
>> Just would like to thank David, Richard  and Steve for their comments on
>> my last query. The two-sided option seems more plausible, indeed.
>>
>> Cheers!
>>
>> Tiago
>>
>>
>>
>>
>> ----------------------------------------------
>> Dear statalisters,
>>
>> I was reading some old post regarding exact tests in Stata and have found
>> the following message:
>>
>> http://www.stata.com/statalist/archive/2005-06/msg00029.html
>>
>> The author of this note comments on the possibility of the Fisher´s exact
>> test for rxc tables available in Stata to be one-tailed. Hence, is it two-
>> or one-tailed?
>>
>> Thanks in advance.
>>
>> All the best,
>>
>> Tiago
>>

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