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FISHER TEST(1)
[Named after the statistician RA Fisher()]. This is an EXACT TEST(1) to examine whether the pattern of counts in a 2x2 cross classification departs from expectations based upon the marginal totals for the rows and columns. Such a test is useful to examine difference in rate between two binomial outcomes. The RANDOMISATION SET consists of those reassignments of the units which produce tables with the same row- and column- totals as the OUTCOME. The RANDOMISATION SET will thus consist of a number of tables with different respective patterns of counts; each such table will have a number of possible RANDOMISATIONS which may be a very large number. For this test there are several reasonable TEST STATISTICs, including : the count in any one of the 4 cells, CHI-SQUARED(1), or the number of RANDOMISATIONS for each 2x2 table with the given row- and column- totals; these are EQUIVALENT TEST STATISTICS. The calculation for the FISHER TEST(1) is relatively undemanding computationally, making reference to the algebra of the hypergeometric distribution, and the test was widely used before the appearance of COMPUTERs. This test has historically been regarded as superior to the use of CHI-SQUARED(2) where sample sizes are small. Statistical tables have been published for the FISHER TEST(1) for a number of small 2x2 tables defined in terms of row- and column- totals. Also see FISHER TEST(2), TWO-WAY TABLE.
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