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Exact randomization tests in their naïve implementation impose a computation burden that makes them generally prohibitive, forcing the researcher to choose between approximate (i.e. incomplete) randomization tests, rank-based tests or normal-family approximations. The algebra and enumeration algorithm for the comparison of two independent means are minutely analysed, and several reduction and acceleration principles are proposed. A sequential back-up mechanism turns out to be the simplest and most efficient to test the difference at the alpha (α) level, with a time-cost generally cut down by a factor better than 1–α.

tutorials in quantitative methods for psychology

Un algorithme efficace pour la comparaison de deux moyennes indépendantes par combinatoire exhaustive; Highly efficient algorithms for the exact randomization test of the difference between two independent means