A Method for Exact Testing of 2X2, 2X3, 3X3, and Other Contingency Tables, Employing Binomial Coefficients

Abstract

Procedures for the computation of the Fisher exact test of 2X2 tables by means of the alignment and multiplication of appropri- ate binomial coefficients are reviewed and extended to larger tables. The 2X3 table originally employed by Freeman and Halton to illustrate their extension of the Fisher exact test principle is reworked with bi- nomial coefficients, their result being obtained with substantially less effort. An example of the application of the method to a 3X3 table is also provided, and the procedures by which the method of binomial co- efficients may be extended to 2XC and RXC tables are outlined.