Multi-level block permutation.
Bottom Line: In a previous study, we defined exchangeability for blocks of data, as opposed to each datum individually, then allowing permutations to happen within block, or the blocks as a whole to be permuted.Here we extend that notion to allow blocks to be nested, in a hierarchical, multi-level definition.The strategy is compatible with heteroscedasticity and variance groups, and can be used with permutations, sign flippings, or both combined.
Affiliation: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK. Electronic address: email@example.com.Show MeSH
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Mentions: Permuting the data freely to test the hypotheses of correlation between thickness or area and indices of body size, therefore not respecting the structure of the sibships, allowed the identification of a few seemingly significant associations, even after fwer correction across the whole brain, and considering that both positive and negative tests were being performed. These regions, shown in Fig. 10, are (1) the left anterior cingulate for a positive correlation between height and cortical surface area, (2) the right orbitofrontal medial cortex for a positive correlation between thickness and bmi, (3), the right temporal pole, at the confluence of the inferior temporal gyrus, for a negative correlation between thickness and body weight, and (4) the right inferior temporal gyrus for a negative correlation between thickness and height. All these regions are very small, two of them comprising just one vertex at the resolution of the surfaces. However, using the proposed multi-level permutation strategy, in which shufflings only happen within siblings of the same type, and in which families with identical structure are allowed to be permuted as a whole, therefore respecting the kinship structure, all these findings became no longer significant. Supplementary Table 3 shows the minimum (most significant) p-value throughout the brain for both unrestricted and restricted permutation.
Affiliation: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK. Electronic address: firstname.lastname@example.org.