Abstract: Background.Commonly, Deep Neural Networks (DNNs) generalize well on samples drawn from a distribution similar to that of the training set. However, DNNs' predictions are brittle and unreliable when the test samples are drawn from a dissimilar distribution.This is a major concern for deployment in real-world applications, where such behavior may come at a considerable cost, such as industrial production lines, autonomous vehicles, or healthcare applications.Contributions.We frame Out Of Distribution (OOD) detection in DNNs as a statistical hypothesis testing problem. Tests generated within our proposed framework combine evidence from the entire network.Unlike previous OOD detection heuristics, this framework returns a $p$-value for each test sample. It is guaranteed to maintain the Type I Error (T1E - incorrectly predicting OOD for an actual in-distribution sample) for test data. Moreover, this allows to combine several detectors while maintaining the T1E.Building on this framework, we suggest a novel OOD procedure based on low-order statistics. Our method achieves comparable or better results than state-of-the-art methods on well-accepted OOD benchmarks, without retraining the network parameters or assuming prior knowledge on the test distribution --- and at a fraction of the computational cost.