R help - Sep 2005 - Fisher's exact test vs Chi-square

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
 
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 
- NOTE NEW EMAIL ADDRESS:
jsorkin@grecc.umaryland.edu
>>> Timothy Mak <Timothy.Mak@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]]

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
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.

Cheers,

Frank
>  
> 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 
> -- NOTE NEW EMAIL ADDRESS:
> 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]]
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
> 

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University