EXACT TESTS OF SIGNIFICANCE IN HIGHER-DIMENSIONAL TABLES

We describe methods used to provide an exact test of significance of t he hypothesis that all factors are mutually independent of each other in 2(3) and 2(4) contingency tables. Several numerical examples demons trate the advantages of exact tests over approximate significance leve ls. We give bounds on the number of tables needed to perform this exac t significance test. In four or more dimensions the number of tables i n this enumeration becomes astronomical with even modest sample sizes. Inverting the characteristic function of the exact distribution has p roved useful in these situations.