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From |
"Tiago V. Pereira" <tiago.pereira@incor.usp.br> |

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". > > I apologize to Tiago for my misleading comments. > > -Steve > > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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