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Resolving the conflict over fisher's exact test
Author(s) -
Routledge R. D.
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315468
Subject(s) - contingency table , exact test , conservatism , binomial (polynomial) , context (archaeology) , mathematics , test (biology) , binomial distribution , continuity correction , econometrics , contingency , statistics , negative binomial distribution , mathematical economics , poisson distribution , epistemology , law , beta binomial distribution , philosophy , paleontology , politics , political science , biology
Fisher's exact test for two‐by‐two contingency tables has repeatedly been criticized as being too conservative. These criticisms arise most frequently in the context of a planned experiment for which the numbers of successes in each of two experimental groups are assumed to be binomially distributed. It is argued here that the binomial model is often unrealistic, and that the departures from the binomial assumptions reduce the conservatism in Fisher's exact test. Further discussion supports a recent claim of Barnard (1989) that the residual conservatism is attributable, not to any additional information used by the competing method, but to the discrete nature of the test, and can be drastically reduced through the use of Lancaster's mid‐ p ‐value. The binomial model is not recommended in that it depends on extra, questionable assumptions.