Permutation Test and FWE Correction. Permutation test is a non-parametric technique that makes minimal assumptions about the data. With few simple assumptions like exchangeability of the observed data under the null hypothesis, the non-parametric permutation test is conceptu- ally simple and theoretically intuitive (Xxxxxxx and Xxxxxxxx, 2003; Xxxxxxx and Xxxxxx, 2001). When the null hypothesis is true, the data will exhibit a form of exchangeability, allowing permutation, re-fitting the model and computation of test statistic. With multiple permutations, an empirical null distribution can be con- structed and critical thresholds and p-values computed. Currently this approach has become well-known and widespread gradually owing to the recent development of inexpensive and powerful computers. nMZ/2 . Σ Applying variance component inference approach voxel-by-voxel yields a test stat- istic image. For each voxel, if the null hypothesis of no heritability, H0 : h2 = 0, is assumed to be true, the MZ and DZ twin pairs become exchangeable, allowing P = (nMZ+nDZ)/2 possible permutations in total. Normally a small-to-medium sample gives a comparatively large P, so an approximate, or Monte Carlo permuta- tion test can be exploited instead with a smaller number of permutations, say N, based on a random subsample of all permutations (Xxxxxxx and Xxxxxx, 2001). In order to resolve the multiple comparisons problem and strictly control the false positives over the whole volume of the ROI’s simultaneously, permutation test can be employed to implement the procedure of FWE correction. Type I errors for all these comparisons are under strong control, and FWE-corrected p-values are computed by considering the maximum test statistics (Xxxxxxx and Xxxxxx, 2001). With a permutation test, we obtain FWE-corrected p-values on peak height (voxel- wise test statistic value) for voxel-wise inference, and cluster size (number of voxels involved in a cluster after thresholding) and cluster mass (sum of voxel-wise test statistic values from all voxels within a cluster after thresholding) for cluster-level inference. Hence, this permutation approach can be further separated into two parts: voxel-wise single threshold test and cluster-wise suprathreshold tests.
