[R] Fisher's exact test vs Chi-square

Frank E Harrell Jr f.harrell at vanderbilt.edu
Tue Sep 13 02:58:41 CEST 2005

John Sorkin wrote:
> Timothy,
> I believe you are mistaken. Fisher's exact test give the correct answer
> even in the face of small expected values for the cell counts. Pearson's
> Chi-square approximates Fisher's exact test and can give the wrong
> answer when expected cell counts are low. Chi-square was developed
> because it is computationally "simple". Fisher's exact test,
> particularly with tables larger than 2 by 2 can be computationally
> complex. The value of the Chi-square statistic becomes closer and closer
> to Fisher's exact test as the expected cell counts become larger.
> John


I'll have to disagree a bit.  Pearson's can still work with low expected 
frequencies.  It was not intended to approximate Fisher's test.  And 
Fisher's is conservative.  The Pearson chi-square with Yates' continuity 
correction was intended to approximate the more conservative Fisher test.



> John Sorkin M.D., Ph.D.
> Chief, Biostatistics and Informatics
> Baltimore VA Medical Center GRECC and
> University of Maryland School of Medicine Claude Pepper OAIC
> University of Maryland School of Medicine
> Division of Gerontology
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> 410-605-7119 
> jsorkin at grecc.umaryland.edu
>>>>Timothy Mak <Timothy.Mak at IOP.KCL.AC.UK> 9/12/2005 11:45:28 AM >>>
> I have heard that people favour the Pearson's Chi-square over Fisher's
> exact test because the latter is more conservative. Some people
> therefore 
> only use Fisher's exact test when some of the expected counts are too 
> small. But nowadays we can quite easily calculate the exact p-value
> based 
> on the Pearson statistic, provided it's not a huge table (SPSS can do
> it). 
> Is there any place for Fisher's exact test then? 
> Tim 
> 	[[alternative HTML version deleted]]
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Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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