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Re: st: Fisher's exact test in r x c contingency tables


From   "Neil Shephard" <mdeasnds@fs1.ser.man.ac.uk>
From   Marcus Keupp <marcus.keupp@unisg.ch>
To   statalist@hsphsun2.harvard.edu
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Fisher's exact test in r x c contingency tables
Subject   st: Fisher's exact test in r x c contingency tables
Date   Thu, 02 Jun 2005 09:49:37 +0100

Date sent:      	Thu, 2 Jun 2005 07:25:20 +0200
Send reply to:  	statalist@hsphsun2.harvard.edu

> Dear Listers,
> 
> in my understanding Fisher's exact test (FET) is applicable in
> 2x2 contingency tables only. However, Stata help contends
> that "... Fisher's exact test ... may be applied to r x c tables
> as well as to 2x2 tables".
> 
> I have heard of some algorithm in SAS that seems to apply FET
> to r x c tables, but I still wonder whether this is appropriate. Is
> Stata maybe computing something similar? The only difference in output
> is that in 2x2 tables, 1- and 2-sided p values are computed, whereas
> in r x c tables one (apparently one-sided) p value only is shown.
> 
> What is your opinion? At the moment I rather think about applying
> tests that were designed for ordinal / ordinal relationships in r x c
> contingency tables (say, Goodman and Kruskal's gamma) than embarking
> on a potentially hazardous procedure.
> 
The original refence for the exact test is I believe Example 1 in Fisher, R. A. (1935). The 
logic of inductive inference. Journal of the Royal Statistical Society Series A 98, 3954 
(obtainable from the Statistics section of 
http://www.library.adelaide.edu.au/digitised/fisher/papers.html which btw has virtually all 
of Fisher's papers which make for some interesting reading).

Neither this paper, or Fisher's "Statistical Methods for Research Wrokers" (to the best 
of my memory, I don't have a copy to hand at the moment), stipulate that the exact test 
is only applicable to 2 x 2 tables, but back then computers weren't so readily available.

I believe the exact tests implemented in Stata are not exactly as the described in the 
above references, as the main problem with applying  Fisher's exact test to r x c tables 
is the exponential increase in computational time required for calculation (for further 
details of exactly how the exact p-values are calculated in r x c tables see the 
references at the end of the help for -tabulate-).

Personally I don't have a problem with applying the exact test to r x c tables, but I 
wouldn't bother trying to apply it to anything with too many dimensions or too large a 
sample size, as the computational time is too long (but see comments under exact 
option in -tabulate-'s help).

HTH's

Neil

Neil Shephard
Genetics Statistician
ARC Epidemiology Unit, University of Manchester
neil.shephard@man.ac.uk
nshephard@gmail.com

"If your result needs a statistician then you should design a better experiment" - 
Ernest Rutherford


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