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


From   sjsamuels@gmail.com
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: st: RE: [iso-8859-1] Fisher´s exact test for rxc [2X2] tables: one-tailed or two-tailed[iso-8859-1] [iso-8859-1] ?
Date   Mon, 4 May 2009 09:01:36 -0400

-
Tiago,

There is support for both positions. The SAS 9.13 Stat manual (page
1473) states" For RxC tables, Fisher's exact test is inherently
two-sided" and that the rejection region consists of  all "all tables
with p less than or equal to the probability of the observed table".
This doesn't make sense to me, as "p" is a tail-probability  not a
table probability.  In any case, I'd have to look up the references
and I don't have time.

As I read the Stata manual (version 10, Ref Q-Z, page 439) correct, it
shows your statement about direction is true for 2x2 tables only.  It
makes a statement about an "algorithm extending this calculation to r
x c tables", but this just about calculating the probabilities of the
tables with R>2 or C>2.  Someone from StataCorp will have to enlighten
us further.

 2x2 tables have a single parameter (odds ratio), about which one can
test directional hypotheses.  For RxC Agresti (2000 p. 56) defines a
minimal (non-unique) set of (R -1)(C-1) odds ratios and states  that
independence  is equivalent to all of these being equal to 1.0.  The
tests of independence will reject if some of them are different from
1.  Some OR could be <1; others >1, but the entire  table itself has
no "direction"-

In all examples that I've seen, the p-value for Pearson chi square,
likelihood-ratio, and Fisher's exact test have been similar with
Pearson closest. The reported Pearson is definitely one-sided-it is
the right-sided tail value. \

So, I guess both interpretations  have some justification.  Until
someone from StataCorp chimes in, feel free to use either.

-Steve

Ref: Alan Agresti, 2000,  Categorical Data Analysis,  Wiley Books.

oOn u, May 2, 2009 at 1:32 PM, Tiago V. Pereira
<tiago.pereira@incor.usp.br> wrote:
> Many thanks, Steve!
>
> But now I am a bit more confused. For example, the Stata exact test for
> rxc tables considers any possible table combination in which the statistic
> is equal or more extreme than that observed by the actual data. However,
> this embraces tables that go in the contrary direction to the observed
> data as well. In other words, the test considers any departure that is
> higher than the observed one. So, this is not a two-sided hypothesis, even
> though the distribution is one-sided?
>
> All the best,
>
> Tiago
>
>
>> 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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