Rapid Acceleration of the Permutation Test via Transpositions

The permutation test is an often used test procedure for determining statistical significance in brain network studies. Unfortunately, generating every possible permutation for large-scale brain imaging datasets such as HCP and ADNI with hundreds of subjects is not practical. Many previous attempts at speeding up the permutation test rely on various approximation strategies such as estimating the tail distribution with known parametric distributions. In this study, we propose the novel transposition test that exploits the underlying algebraic structure of the permutation group. The method is applied to a large number of diffusion tensor images in localizing the regions of the brain network differences.