An Algorithm to Compute Exact Power of an Unordered RxC Contingency Table

Chi-square, Likelihood Ratio and Fisher-Freeman-Halton test statistics are used to test the association of an unordered rxc. Although asymptotically all these statistics follow a chi-square distribution, an exact conditional test based on the permutation distribution is recommended for small samples. The exact power computation of such tests involves huge numbers of permutation tables, and as a result computation becomes infeasible. The asymptotic power computation of these methods can be done using a non-central chi-square test (see Agresti A, 2002: Categorical Data Analysis). However, to our knowledge, there is no algorithm/method available to compute the exact power. In this article we give an efficient algorithm and a SAS macro to compute exact power using Chi-square, Likelihood Ratio and Fisher-Freeman-Halton test statistics. The SAS macro also reports exact power for the Mid-P and the randomized versions of the tests.