[S] Fisher's exact test isn't always appropriate

Frank E Harrell Jr (fharrell@virginia.edu)
Wed, 25 Mar 1998 11:53:16 -0500

There seems to be a tremendous interest in Fisher's exact test.
At the risk of setting off a religious war please let me note a few points:

1. Fisher's test is a conditional test whereas we're usually interested in unconditional
tests (i.e., not conditioning on the margins)
2. The test can be conservative - see

author = "D'Agostino, R. B. and Chase, W. and Belanger, A.",
journal = American Statistician,
pages = "198-202",
title = "The appropriateness of some common procedures for testing the equality of two independent binomial populations",
volume = "42",
year = "1988",
annote = "Logistic model, discriminant analysis, binary random var., Statistical computation algorithms"

3. The rule of "expected value of 5 in each cell' to be able to use Pearson's chi-square
is too stringent in many cases.

The default test I use is the likelihood ratio test. There are newer promising unconditional
tests that I hope to learn about.

Frank E Harrell Jr
Professor of Biostatistics and Statistics
Director, Division of Biostatistics and Epidemiology
Dept of Health Evaluation Sciences
University of Virginia School of Medicine

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