Negative probabilities and contextuality

There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is Contextuality-by-Default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with Contextuality-by-Default and by examining with this theory some simple examples where contextuality appears, both in physics and psychology.