Date:         Fri, 3 Oct 2003 08:58:47 -0500
Reply-To:     Anthony Babinec <tbabinec@ameritech.net>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Anthony Babinec <tbabinec@ameritech.net>
Subject:      FW: Asymptotic significant in Chi-square test
Content-Type: text/plain; charset="US-ASCII"

In the special case of the test of equality of two
binomial probabilities, there are two exact tests:
the Fisher exact test and Barnard's test.  Fisher's
test conditions on the table marginals, while Barnard's
test is unconditional.  Research has shown that the
Barnard test has more statistical power.  See the
article by Mehta and Senchaudhuri at

http://www.cytel.com/new.pages/sept_newsletter_home.html

To relate this to SPSS, SPSS Base CROSSTABS makes available
only the Fisher exact test for the 2x2 table.  SPSS Exact Tests
makes available exact p-values for various chi-square statistics
for r by c tables.

Anthony Babinec


-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of
Gilles Gignac
Sent: Thursday, October 02, 2003 11:56 PM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Re: Asymptotic significant in Chi-square test


It is perhaps a myth that Fisher's Exact test is better than Pearson's
chi-square, because it provides an "exact" p value. Fisher's Exact test
should only be considered a gold standard for the 2*2 case, when one is
dealing with fixed marginals. The statistic is based on the hypergeometric
distribution. An example would be a study where a blind folded person is
required to sort a deck of cards into two equal piles of red and black
cards. According to the literature, it is only in the case of fixed
marginals that one should use Fisher's Exat test, and the reason is because,
according to monte carlo research, Fisher's Exact test is much too
conservative to be used in the place of Pearson's chi-square: the type II
error rate is too high. Most researchers will never be presented with data
approrpriate for Fisher's exact test (ie., fixed marginals)

Pearson's chi-square is more robust than many people may believe. Some monte
carlo research has demonstrated the statistic to be robust even for expected
cell frequencies as low as 1.3 (N = 20, 3*5). Further, even under extreme
circumstances (N = 20, 3*3*3), the type one error rate seems to peak at
about .09.

Finally, and to relate this to SPSS somehow, Ray Newcombe has written a
freely available script to analyze proportions for SPSS. It provides a 95%
confidence interval for the difference between two proportions. In my
opinion, most people would be better off analyzing a 2*2 contingency table
from the a proportions perspective, which can circumvent the whole issue of
minimum expected cell frequencies. Here's the link to Newcombe's site with
the script.

http://www.uwcm.ac.uk/study/medicine/epidemiology_statistics/research/statis
tics/proportions.htm

References: Farone, Stephen, (1982). American PSychologist, 107.

Rhoades, and Overall. (1982). Psychological Bulletin, 91(2), 418-423.

Camilli, and Hopkins. (1978). Psychological Bulletin, 85, (1), 163-167

Gilles