While the distribution-free nature of permutation tests makes them the most appropriate method for hypothesis testing under a wide range of conditions, their computational demands can be runtime prohibitive, especially if samples are not very small and/or many tests must be conducted (e.g. all pairwise comparisons). This paper presents statistical code that performs continuous-data permutation tests under such conditions very quickly often more than an order of magnitude faster than widely available commercial alternatives when many tests must be performed and some of the sample pairs contain a large sample. Also presented is an efficient method for obtaining a set of permutation samples containing no duplicates, thus maximizing the power of a pairwise permutation test under a conventional Monte Carlo approach with negligible runtime cost (well under 1% when runtimes are greatest). For multiple comparisons, the code is structured to provide an additional speed premium, making permutation-style p-value adjustments practical to use with permutation test p-values (although for relatively few comparisons at a time). No-replacement sampling also provides a power gain for such multiple comparisons, with similarly negligible runtime cost.
Opdyke, J. D.
"Fast Permutation Tests that Maximize Power Under Conventional Monte Carlo Sampling for Pairwise and Multiple Comparisons,"
Journal of Modern Applied Statistical Methods:
1, Article 5.
Available at: http://digitalcommons.wayne.edu/jmasm/vol2/iss1/5