Abstract

We consider a finite sample density test for the continuity of a density function at a point. Specifically, we derive the worst-case density function that achieves the worst-case rejection probability under a Lipschitz class so that we may control the size of the test in a finite sample. We extend our analysis to consider non-increasing and Lipschitz continuous densities on [0,1]. We apply our procedure to a p-hacking detection problem using a dataset of tests reported in top Economics publications.