Abstract
Benford's law states that the frequency of first significant digits (FSD) in a random sample decreases as those digits increase. While this curious law is increasingly used to test for human influence on data, including corporate fraud and psychological barriers in financial markets, it often produces frustratingly many false positives. I advance toward the goal of understanding and reducing the false alarm rate by showing that Benford's law is inadequate when data are drawn from various common distributions, including the ubiquitous normal distribution. I also prove that Benford's law is obeyed when the untainted data are lognormally distributed with a high variance parameter. In addition, I explain why data sets expressible as the product of two other sets often conform better to Benford's law than either multiplicand data set. The empirical analysis strongly supports these findings.