Severe testing of Benford's law

This paper contributes to the debate on Benford's law testing by proposing a method to overcome the "excess power problem" critique, so widespread in this literature. In particular we suggest using the notion of severity testing (Mayo & Spanos, 2006) in the framework of tests for conformity with Benford's law. To do so, we also derive the asymptotic distribution of Nigrini's mean absolute deviation statistic (MAD, Nigrini, 2012) and an asymptotic standard normal test. Finally, the severity testing principle is applied to six controversial data sets to assess their "Benford-ness".