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Language models (LMs) show state of the art performance for common sense (CS) question answering, but whether this ability implies a human-level mastery of CS remains an open question. Understanding the limitations and strengths of LMs can help researchers improve these models, potentially by developing novel ways of integrating external CS knowledge. We devise a series of tests and measurements to systematically quantify their performance on different aspects of CS. We propose the use of cloze testing combined with word embeddings to measure the LM's robustness and confidence. Our results show than although language models tend to achieve human-like accuracy, their confidence is subpar. Future work can leverage this information to build more complex systems, such as an ensemble of symbolic and distributed knowledge.