Benford's Law

Post Date: 6/21/13
Last Updated: 6/20/13


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The following article is entirely an author’s comment. Information presented should be considered the opinion of the author and not that of an authoritative citation.

Have you ever heard of Benford’s Law? I had never heard of it until reading an article in a recent trade journal written for tax accountants. I did not pay much attention to the article until it was pointed out that the IRS mentions it in their Internal Revenue Manual, Part 4, Examining Process, Section, PAC Inventory Sources, letter L, which says: “Benford’s Law Analysis—used to identify problematic preparers.”

Mention “problematic preparers,” and with all the possible preparer penalties facing our profession, I took notice. How does Benford’s law identify problematic preparers?

Benford’s law is also called the first-digit law, and refers to the frequency distribution of digits in many real-life sources of data. The law predicts the percentage of time a particular digit will occur as the first digit in a data set of numbers, assuming the data set is a random set of numbers and not made up by some human. For example, the number 1 occurs as the leading digit about 30% of the time, while the number 9 occurs as the leading digit about 5% of the time. The law is based upon a mathematical formula and is named after physicist Frank Benford. The results of the mathematical formula are contained in the following table:

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