Abstract The reproducibility crisis in neuroimaging and in particular in the case of underpowered studies has introduced doubts on our ability to reproduce, replicate and generalize findings. As a response, we have seen the emergence of suggested guidelines and principles for neuroscientists known as Good Scientific Practice for conducting more reliable research. Still, every study remains almost unique in its combination of analytical and statistical approaches. While it is understandable considering the diversity of designs and brain data recording, it also represents a striking point against reproducibility. Here, we propose a non-parametric permutation-based statistical framework, primarily designed for neurophysiological data, in order to perform group-level inferences on non-negative measures of information encompassing metrics from information-theory, machine-learning or measures of distances. The framework supports both fixed- and random-effect models to adapt to inter-individuals and inter-sessions variability. Using numerical simulations, we compared the accuity in ground-truth retrieving of both group models, such as test- and cluster-wise corrections for multiple comparisons. We then reproduced and extended existing results using both spatially uniform MEG and non-uniform intracranial neurophysiological data. We showed how the framework can be used to extract stereotypical task- and behavior-related effects across the population covering scales from the local level of brain regions, inter-areal functional connectivity to measures summarizing network properties. We also present a open-source Python toolbox called Frites 1 that includes all of the methods used here, from functional connectivity estimations to the extraction of cognitive brain networks. Taken together, we believe that this framework deserves careful attention as its robustness and flexibility could be the starting point toward the uniformization of statistical approaches. Graphical abstract Highlights We introduce a statistical framework for the characterisation of cognitive brain networks through group-level inference of measures of information computed on neurophysiological data The framework supports both fixed- and random-effect models, test- and cluster-wise corrections based on non-parametric permutations The framework can serve statistical inferences at multiple levels from local brain regions to inter-areal functional connectivity and graph theoretical metrics A Python open-source toolbox called Frites includes the proposed statistical methods ( https://github.com/brainets/frites )