As part of the AP process, a reasonable review to detect fraud in your nonprofit organization should be part of the procedures.  In previous blog articles, NFP Partners has discussed ways to mitigate fraud, such as proper checks and balances, segregation of duties, vendor verification, etc.  We would like to offer your nonprofit organization another great way to detect fraud by using statistical methods, such as Benford’s Law.

What is it Benford’s Law?     

Benford’s Law, which was first mentioned in 1881 by the astronomer Simon Newcomb, states if we randomly select a number from a table of physical constants or statistical data, the probability that the first digit will be a one is about 0.301, rather than 0.1 as we might expect if all digits were equally likely. This numerical phenomenon was published by Newcomb in a paper entitled “Note on the Frequency of Use of the Different Digits in Natural Numbers,” which appeared in The American Journal of Mathematics (1881) 4, 39-40. It was re-discovered by Benford in 1938, and he published an article called “The Law of Anomalous Numbers” in Proc. Amer. Phil. Soc 78, pp 551-72.

How can Benford’s Law help my nonprofit organization identify fraud?

If we know the normal frequency of digits, then we can identify digit frequencies that violate that normal behavior. For example, Benford concluded that, out of a group of numbers, the first digit will be one about 30 percent of the time. Similarly, using the same function, we can expect the first digit to be eight about 5.1 percent of the time. Expected frequencies for each first-digit of the invoice amount are shown in the table below:

Leading digit Benford’s Law
1 30.1%
2 17.6%
3 12.5%
4 9.7%
5 7.9%
6 6.7%
7 5.8%
8 5.1%
9 4.6%

An excel file can be created to drop in the first digit of the amount of each check and then count the frequency of each number. Then, take that count and divide it by the sum to give the % of each number. Compare the probability percentages in the AP check run against the Benford’s Law percentage. If the large anomaly in the data is calculated, it doesn’t necessarily mean the data is fraudulent. It would, however, provide a good reason for further investigation. Most of the time, a simple AP report with the vendor and check data will uncover a specific reason for the anomaly. For example, each month a nonprofit reimburses employees $70 for extra duty pay. On that day, you will expect to see the number seven more frequently than a normal check run.

How your nonprofit can “trust but verify”

Most employees are trustworthy! But, it doesn’t hurt to conduct some data mining to objectively evaluate the fraud potential. If your nonprofit has the proper procedures in place, it can significantly reduce fraudulent activities from occurring or cut losses if fraud has already occurred. Making the organization policy known to employees is one of the best ways to deter fraudulent behavior. If fraud is uncovered, following through with the policy and enforcing the noted steps and consequences is crucial to preventing fraud in the future.


Mandy Potts,
Director of Business Development