Newsgroups: bit.listserv.stat-l
Date:         Wed, 2 Sep 1992 07:12:52 -0400
From:         712_dbh3@WHITE.WHOI.EDU
X-To:         stat-l@mcgill1.bitnet@MAILHOST.span.nasa.gov

I would like to thank all of those who replied to my query regarding
the power of Fisher's exact test relative to tests such as chi-square
or log-likelihood chi-squares.


To summarize the responses, there does not appear to be a consensus on the
actual power of Fisher's test compared to the alternatives.  Some
people indicate that Fisher's test is "the" answer, and the
apparently higher power of other tests is due to their being too
liberal for small sample sizes.  Other individuals have pointed to
recent studies suggesting that Fisher's test truly does lack power
relative to the alternatives, even for small sample sizes.

Several points brought out by those who replied are very pertinent,
in particular:

  - The version of Fisher's exact test referred to in Kendall and
    Stuart is a randomized version of the test which is not the
    test that is generally applied in practice.  Accordingly, their
    statements that this test is Uniformly Most Powerful Unbiased
    does not necessarily apply to the non-randomized version of the
    test.

  - Much of the difference in opinion in power of the tests appears
    to be more fundamental than which test to use.  Rather, the
    preliminary question to be answered is "are fixed marginal
    totals most appropriate for inference in this situation".
    Being relatively new to the list, I have apparently missed
    prior discussions on the appropriateness of fixed marginal totals.

  - Other "exact" tests exist which do not make the assumption of
    fixed marginal totals.  These are less familar to many people
    than Fisher's test, but offer an alternative to chi-square
    type of approximations when one does not wish to take the
    philosophy that fixed marginal totals is "the" way to
    analyze contingency tables.

 -  Some folks were unaware of the development of analogs to
    Fisher's exact test for contingency tables greater than
    2x2.  References to these methods are included later in this
    message, and have been implemented in SAS version 6.04 as well
    as some other statistical packages.

Some references (not all of which are available in our local
library but which I am passing along as potentially useful) are:


 Boschloo, R. D. (1970).  "Raised conditional level
      .," Statistica Neerlandica, vol. 24, 1-35.

Bennett and Hsu. 1960.  On the power function of the exact test for the
    2x2 contingency table.  Biometrika 47:393-397.

Chapman.  1976.  A comparison of the X2, -2 log R, and ... when expected
   frequencies are small.  JASA 71:854-863

D'Agostino et al.  1988.  The appropriateness of some common procedures...
   American Statistician 42:198-202.

Haberman.  1988.  A warning on the use of chi-square ... small expected cell
   counts.  JASA 83:555-560.

Little.  1989.  Testing the equality of two independent binomial proportions.
  American Statistician 43:283-288.

  Mehta, C. R., and N.R. Patel.  1983.  A network algorithm for performing
 Fisher
     's exact test in r x c contingency tables. JASA 78:427-434.

  Pagano, M., and K. T. Halvorson.  1981.  An algorithm for finding the exact
      significance levels of r x c contingency tables.  JASA 76:931-934.

Storer and Kim.  1990.  Exact properties of some exact test statistics for
  comparing two binomial proportions.  JASA 85:146-155.

Zelterman.  1987.  Goodness-of-fit tests for large sparse multinomial distri-
  butions.  JASA 82:624-629.



I hope this summary is useful. Additional insight into this problem is
appreciated.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU