Premium
On Conditions for Validity of the Approximations to Fisher's Exact Test
Author(s) -
Martínandrés A.,
Tejedor I. Herranz
Publication year - 1997
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710390806
Subject(s) - exact test , test (biology) , mathematics , poisson distribution , binomial (polynomial) , table (database) , chi square test , exact statistics , calculus (dental) , statistics , computer science , data mining , medicine , paleontology , dentistry , biology
A 2 × 2 table is analyzed from the conditional viewpoint, using Fisher's exact test, for which there is abundant software nowadays (StatXact, SPSS with the module “Exact Test”, …). Nevertheless, because it is well‐nigh impossible to work the test out “by hand”, it is customary in many books to analyze the table, in an approximate fashion, by using the classic chi‐square test with the appropriate continuity correction, and this is what many researchers do in practice. Unfortunately little research has been carried out on the validity conditions of the test (remember the classic advice that the minimum expected quantity E should be larger than or equal to 5), so that it is applied indiscriminately with the obvious danger of obtaining erroneous results. In this paper the exact validity conditions (which depend not only on E , but also on the real P‐value, on the size of the sample, on the number of tails of the test and on the continuity correction used) are determined, showing that the classic condition E > 5 can be either very strict or quite liberal (depending on the circumstances) and it can even be necessary for the test to have E > 20. A similar study is made of the case of using the binomial approximation, while the Poisson approximation is also discussed. The article ends with a list of rules and precautions to be borne in mind by researchers using the approximate methods. The strict rules are complex enough to make the researcher want to use the exact test, but simplified (and conservative) rules are also given for those unable to do so.