A nonasymptotic analysis algorithm based on Pearson's chi-square statistic is presented to investigate r by c contingency tables where small expected cell frequencies render the usual asymptotic analysis inappropriate. Following computation of the exact mean, variance, and skewness of this statistic under the conditional permutation distribution, the Pearson type III distribution yields the P value. A FORTRAN subroutine is provided for analyzing the all too frequently encountered r by c contingency tables involving either highly disproportionate marginal totals or relatively small marginal totals.