Permutation tests for factorially designed neuroimaging experiments

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Abstract
Permutation methods for analysis of functional neuroimaging data acquired as factorially designed experiments are described and validated. The F ratio was estimated for main effects and interactions at each voxel in standard space. Critical values corresponding to probability thresholds were derived from a null distribution sampled by appropriate permutation of observations. Spatially informed, cluster‐level test statistics were generated by applying a preliminary probability threshold to the voxel F maps and then computing the sum of voxel statistics in each of the resulting three‐dimensional clusters, i.e., cluster “mass.” Using simulations comprising two between‐ or within‐subject factors each with two or three levels, contaminated by Gaussian and non‐normal noise, the voxel‐wise permutation test was compared to the standard parametric F test and to the performance of the spatially informed statistic using receiver operating characteristic (ROC) curves. Validity of the permutation‐testing algorithm and software is endorsed by almost identical performance of parametric and permutation tests of the voxel‐level F statistic. Permutation testing of suprathreshold voxel cluster mass, however, was found to provide consistently superior sensitivity to detect simulated signals than either of the voxel‐level tests. The methods are also illustrated by application to an experimental dataset designed to investigate effects of antidepressant drug treatment on brain activation by implicit sad facial affect perception in patients with major depression. Antidepressant drug effects in left amygdala and ventral striatum were detected by this software for an interaction between time (within‐subject factor) and group (between‐subject factor) in a representative two‐way factorial design. Hum. Brain Mapping 22:193–205, 2004.