Empirical Sampling from Permutation Space with Unique Patterns

The exact distribution of a test statistic ultimately guarantees that the probability of a Type I error is exactly α. Several methods for estimating the exact distribution of a test statistic have evolved over the years with inherent computational problems and varying degrees of accuracy. The unique pattern of permutations resulting from using experimental data to sample within the permutation space without the risk of repeating permutations is identified. The method presented circumvents the theoretical requirements of asymptotic procedures and the computational difficulties associated with an exhaustive enumeration of permutations. Results show that time and space complexities are drastically reduced without compromising accuracy even when enumeration is not exhaustive provided error tolerance is achieved. The exact distribution of the Siegel-Tukey test statistic is examined as an illustration