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

 From "Tiago V. Pereira" To statalist@hsphsun2.harvard.edu Subject Re: st: RE: [iso-8859-1] Fisher´s exact test for rxc [2X2] tables: one-tailed or two-tailed Date Sun, 3 May 2009 22:47:40 -0300 (BRT)

```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".
>
>
> -Steve
>
>

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