Multiscale null hypothesis testing for network‐valued data: Analysis of brain networks of patients with autism

Networks are a natural way of representing the human brain for studying its structure and function and, as such, have been extensively used. In this framework, case–control studies for understanding autism pertain to comparing samples of healthy and autistic brain networks. In order to understand the biological mechanisms involved in the pathology, it is key to localize the differences on the brain network. Motivated by this question, we hereby propose a general non‐parametric finite‐sample exact statistical framework that allows to test for differences in connectivity within and between prespecified areas inside the brain network, with strong control of the family‐wise error rate. We demonstrate unprecedented ability to differentiate children with non‐syndromic autism from children with both autism and tuberous sclerosis complex using electroencephalography data. The implementation of the method is available in the R package nevada .