![]() The paper includes a flow chart prescribing these various approaches for each case, reproduced below. These methods are available in the tool PALM - Permutation Analysis of Linear Models- and the complete description, evaluation, and application to the re-analysis of a voxel-based morphometry study (Douaud et al., 2007) have been just published in Winkler et al., 2016 (for the Supplementary Material, click here). In addition to accelerating permutation tests, some of these strategies, such as tail and noperm, allow continuous p-values to be found, and refine the p-values far into the tail of the distribution, thus avoiding the usual discreteness of p-values, which can be a problem in some applications if too few permutations are done. Some, such as tail approximation, are generic enough to be used nearly all the most common scenarios, including univariate and multivariate tests, spatial statistics, and for correction for multiple testing. These strategies allow accelerations >100x, yielding nearly identical results as in the non-accelerated case.
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