In out-of-distribution (OOD) detection, one is asked to classify whether a test sample comes from a known inlier distribution or not. We focus on the case where the inlier distribution is defined by a training dataset and there exists no additional knowledge about the novelties that one is likely to encounter. This problem is also referred to as novelty detection, one-class classification, and unsupervised anomaly detection. The current literature suggests that contrastive learning techniques are state-of-the-art for OOD detection. We aim to improve on those techniques by combining/ensembling their scores using the framework of null hypothesis testing and, in particular, a novel generalized likelihood ratio test (GLRT). We demonstrate that our proposed GLRT-based technique outperforms the state-of-the-art CSI and SupCSI techniques from Tack et al. 2020 in dataset-vs-dataset experiments with CIFAR-10, SVHN, LSUN, ImageNet, and CIFAR-100, as well as leave-one-class-out experiments with CIFAR-10. We also demonstrate that our GLRT outperforms the score-combining methods of Fisher, Bonferroni, Simes, Benjamini-Hochwald, and Stouffer in our application.