Gurevich and Vladimir Vovk

While p-values are widely used and discussed, we do not know a careful de nition of the concept in the literature. We sought to ll in the gap. In the process we discovered that the traditional notion of test statistic is too narrow, and this article indicates a natural generalization. An older version of this paper is published as an arXiv technical report: https: //arxiv.org/abs/1702.02590.