Arizona, 1992. The State Treasurer’s Office. A manager siphons off nearly $1.9M by writing cheques to fictitious suppliers. He thinks he is untouchable, until the day an accountant applies Benford’s law to his transactions. Stunning revelation: more than 90% of the fraudulent amounts start with 7, 8 or 9. A glaring statistical aberration. The manager is arrested, the evidence mathematically damning. This is the case said to have inspired Nigrini.
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At an American bank, a routine audit reveals an abnormal cluster of transactions starting with 48 and 49. Following the thread, investigators uncover an ingenious scheme. A complicit bank officer was getting credit cards issued to his friends. They ran up debts just under $5,000, the critical threshold above which extra approval was required. The officer then wrote those debts off the books. The abnormal first-digit distribution gave him away. The invisible signature of his fraud was right there, written into the numbers like a mathematical confession.
In Detroit, a financial controller at a pharmaceutical company had created thousands of fictitious refunds. For all his creativity in varying the amounts, the even distribution of first digits screamed fraud. He had tried to simulate chance, unaware that true chance is never even.
The method eventually caught on beyond the corridors of the IRS. The Securities and Exchange Commission uses it to detect accounting manipulation at listed companies. The FBI adds it to its arsenal against financial crime. Insurers apply it to suspicious claims. Insurance fraud, falsified prices, doctored financial reports - all of it can be analysed with a method that needs nothing more than data gathered in a simple spreadsheet.
In the fraud detector’s toolkit, Benford’s law has become a must. The statistical approach follows a relentless logic. A null hypothesis: the data has not been tampered with. An alternative hypothesis: the data has been manipulated. In between, a mathematical test, the chi-square, which measures the gap between the distribution expected under Benford and the distribution observed in the suspect data.
The beauty of the method? It works without understanding what the data is about. Tax returns, medical bills or expense reports, it makes no difference. The maths detects human intervention in what should be a natural process. Simply by calculating the difference between observed and expected frequencies, squaring it, then dividing by the expected frequencies, you get a precise measure of the anomaly.
When the calculated value exceeds a predetermined critical threshold, the red light comes on. Experts then look at the data with fresh eyes. Benford’s law accuses no one directly; it simply points to the areas that deserve a closer look.