Reality Checks for a Distributional Assumption: The Case of “Benford’s Law”

In recent years, many articles have promoted uses for “Benford’s Law,” claimed to identify a nearly ubiquitous distribution pattern for the frequencies of first digits of numbers in many data sets. Detecting fraud in financial and scientific data is a suggested application. Like the Normal and Chi-square distributions, Benford’s appears to offer an appealingly clear-cut, mathematically tractable, and widely applicable tool. However, similar to those other models, writers may “assume” the model meets all the assumptions needed for hypothesis testing, without properly examining whether those conditions hold. This paper examines a diverse set of real-world data sets to demonstrate that while Benford’s-like patterns are indeed common, Benford's per se is not a unique and universal template for all cases of interest to fraud investigators. This reminds us of how, in general, distributional assumptions can sometimes be overlooked or fail to be critically questioned.