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 nonnegative 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 accuracy 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 an open-source Python toolbox called Frites 1 that includes the proposed statistical pipeline using information-theoretic metrics such as single-trial functional connectivity estimations for 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.