Resumen de Applying and Testing Benford’s Law Are Not the Same
William M. Goodman
Most papers on Benford’s Law primarily discuss either (1) the science and mathematics for explaining the law; or (2) how to apply the law, especially for detecting data manipulation and fraud; or (3) suggestions for statistical tests to determine if data conform to a Benford’s distribution. Leonardo Campanelli’s recent paper “Testing Benford’s Law” strongly objects to a descriptive measure I discussed in my paper “The Promises and Pitfalls of Benford’s Law”—as if that measure were intended for Benford’s testing in the Category-3 sense relevant for Campanelli’s paper (SJS, vol. 4, 2022). This reflects a conflation of meanings for “testing” that is common in the Benford’s literature, where many Category-2 papers claim they are applying (directly) conventional or new hypothesis tests as tools to detect fraud. Yet, fraud detection is a forensic and context-sensitive process, for which there is no set formula. In this paper, I clarify the sampling plan I had used earlier to collect and analyze a quasi-random sample of datasets, based on published criteria in the literature, to paint a tentative picture of how far real data vary, and in what ways, from abstract BL expectations. Further, I discuss simulations I have conducted to replicate and expand on my previous results.
