Using Benford's Law for Fraud Detection and Auditing
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This presentation will explain the theory behind Benford's law and how it can be used to find errors or potential fraud . SLIDESHARE: www.slideshare.net/CaseWare_Analytics WEBSITE: www.casewareanalytics.com BLOG: www.casewareanalytics.com/blog TWITTER: www.twitter.com/CW_Analytic
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Using Benford's Law for Fraud Detection and Auditing
- 1. USING BENFORD’S LAW FOR FRAUD DETECTION & AUDITING
- 2. AGENDA • What is Benford’s Law? • Conforming/Non-Conforming Data Types • Practical Applications of Benford’s Law • Major Digit Tests
- 3. FROM THEORY TO APPLICATION Timeline • 1881- Simon Newcomb • 1938 – Frank Benford • 1961 - Roger Pinkham • 1992 - Mark Nigrini Simon Newcomb: Looked at frequency of use of the different digits in natural numbers - “A multi-digit number is more likely to begin with ‘1’ than any other number.”
- 4. FROM THEORY TO APPLICATION Timeline • 1881- Simon Newcomb • 1938 – Frank Benford • 1961 - Roger Pinkham • 1992 - Mark Nigrini Frank Benford: Analyzed 20,229 sets of numbers, including, areas of rivers, baseball averages, atomic weights, electricity bills, and more - Multi digit numbers beginning with 1, 2 or 3 appear more frequently than multi digit numbers beginning with 4, 5, 6,...
- 5. FROM THEORY TO APPLICATION Timeline • 1881- Simon Newcomb • 1938 – Frank Benford • 1961 - Roger Pinkham • 1992 - Mark Nigrini Data Sets First Digit = 1 First Digit = 2 First Digit = 3 Populations 33.9 20.4 14.2 Batting averages 32.7 17.6 12.6 Atomic weight 47.2 18.7 10.4 X-ray volts 27.917 15.7 Average 30.6% 18.5% 12.4%
- 6. FROM THEORY TO APPLICATION Timeline • 1881- Simon Newcomb • 1938 – Frank Benford • 1961 - Roger Pinkham • 1992 - Mark Nigrini Roger Pinkham: Research conducted revealed that Benford’s probabilities are scale invariant. Dr. Mark Nigrini: Published a thesis noting that Benford’s Law could be used to detect fraud because human choices are not random, invented numbers are unlikely to follow Benford’s Law.
- 7. BENFORD’S LAW The number 1 occurs as the leading digit 30.1% of the time, while larger numbers occur in the first digit less frequently. For example, the number 3879 • 3 - first digit • 8 - second digit • 7 - third digit • 9 – fourth digit
- 8. BENFORD’S LAW KEY FACTS • For naturally occurring numbers, the leading digit(s) is (are) distributed in a specific, non-uniform way. • While one might think that the number 1 would appear as the first digit 11 percent of the time, it actually appears about 30 percent of the time. • Therefore the number 1 predominates most progressions. • Scale invariant – works with numbers denominated as dollars, yen, euros, pesos, rubles, etc. • Not all data sets are suitable for analysis.
- 10. DATA TYPES • Data set should describe similar data (e.g. town populations) • Large data sets • Data that has a wide variety in the number of figures e.g. plenty of values in the hundreds, thousands, tens of thousands, etc. • No built-in maximum or minimum values • Some common characteristics of accounting data…
- 11. CONFORMING DATA TYPES • Accounts payable transactions • Credit card transactions • Customer balances and refunds • Disbursements • Inventory prices • Journal entries • Loan data • Purchase orders • Stock prices, T&E expenses, etc.
- 12. NON-CONFORMING DATA TYPES • Data where pre-arranged, artificial limits or numbers influenced by thought exist, i.e. built-in max or min values • Zip codes, telephone nos., YYMM#### as insurance policy no. • Prices sets at thresholds ($1.99, ATM withdrawals, etc.) • Airline passenger counts per plane • Aggregated data • Data sets with 500 or few transactions • No transaction recorded - Theft, kickback, skimming, contract rigging, etc.
- 13. USAGE OF BENFORD’S LAW Within a comprehensive Anti-Fraud Program Risk Assessment Control Environment Control Activities Information and Communication Specify organizational objectives Monitoring COSO Framework
- 14. BENFORD’S IN RISK-BASED AUDITS • Early warning sign that past data patterns have changed or abnormal activity Data Set X represents the first digit frequency of 10,000 vendor invoices.
- 15. USE IN RISK-BASED AUDITS • Risk-based audits - Early warning sign that past data patterns have changed or abnormal activity Data Set X represents the first digit frequency of 10,000 vendor invoices.
- 16. USE IN OTHER AUDITS • Forensic audits - Check fraud, bypassing permission limits, improper payments • Audit of financial statements - Manipulation of checks, cash on hand, etc. • Corporate finance/company evaluation - Examine cash- flow-forecasts for profit centers
- 17. USING DATA ANALYTICS (IDEA) • 1st Digit Test • 2nd Digit Test • First two digits • First three digits • Last two digits • Second Order Test
- 18. 1ST AND 2ND DIGIT TESTS 1st Digit Test • High Level Test - Will only identify the blinding glimpse of the obvious • Should not be used to select audit samples, as the sample size will be too large 2nd Digit Test • Also a high level test - Used to identify conformity • Should not be used to select audit samples
- 19. FIRST TWO DIGITS TEST • More focused and examines frequency of numerical combinations 10 through 99 on the first two digits of a series of numbers • Can be used to select audit targets for preliminary review Example: 10,000 invoices -- > 2,600 invoices -- > (1.78% + 1.69%) x 10,000 -- > (178 + 169) = 347 invoices Only examine invoices beginning with the first two digits 31 and 33.
- 20. FIRST THREE DIGITS TEST • Highly Focused - Used to select audit samples • Tends to identify number duplication
- 21. LAST TWO DIGITS TEST • Used to identify invented (overused) and rounded numbers • Expected that right-side two digits be distributed evenly. With 100 possible last two digits numbers (00, 01, 02...., 98, 99), each should occur approximately 1% of time Source: Fraud and Fraud Detection: A Data Analytics Approach, John Wiley & Sons, Inc., Hoboken, New Jersey Source: Fraud and Fraud Detection: A Data Analytics Approach, John Wiley & Sons, Inc., Hoboken, New Jersey
- 22. SECOND ORDER TEST • Based on the 1st two digits in the data. • A numeric field is sorted from the smallest to largest and value differences between each pair of consecutive records should follow the digit frequencies of Benford’s Law. Source: Fraud and Fraud Detection: A Data Analytics Approach, John Wiley & Sons, Inc., Hoboken, New Jersey
- 23. SUMMARY • Benford Law works well to detect invented numbers when: • One person invents all the numbers • Lots of different people have an incentive to manipulate numbers in the same way • Useful first step to give a better understanding of our data • Need to use Benford’s Law with other drill down tests to detect fraud, errors, biases, and other anomalies • Technology enables faster and easier to produce results
- 24. WANT TO SEE BENFORD’S LAW IN IDEA? Contact us at [email protected] to schedule a demonstration
- 25. USING BENFORD’S LAW FOR FRAUD DETECTION & AUDITING Visit casewareanalytics.com Email [email protected]
Editor's Notes
- #11: Benford’s Law does not apply to all sets of numbers. For it to apply the numbers must reflect the size of some phenomenon; big numbers must refer to big things. There must be no built-in maximum or minimum values. Tax returns have minimum or maximum amounts in various places. The numbers must not be labels such as highway numbers, social security numbers, or flight numbers. Accounting Data usually conforms.
- #20: Examines the frequency of the numerical combinations 10 through 99 on the first two digits of a series of numbers. In particular the output serves for the analysis of avoided threshold values. Thus, these tests help to clearly visualize when order or permission limits have been systematically avoided Example: We detected an abundance of invoices beginning with 3. Based upon that review, we need to examine approximately 2,600 invoices. However, using the first two digits test, we can see that not all of the invoices need to be examined. Instead, we need only examine those invoices beginning with the first two digits 31 and 33. As you can see in the chart, these are the first two digits whose actual frequencies differ the most from their expected frequencies (-.40 and -.39, respectively). Therefore, if we focus on numbers beginning with 31 or 33, we only need to review 347 (178 + 169) invoices. This was calculated by multiplying 1.78% (actual frequency percentage for the first two digits 31) by 10,000 (number of total invoices) and adding that to 1.69% (actual frequency percentage for the first two digits 33) times 10,000 (number of total invoices). This test results in a required audit sample of more than 2,000 fewer invoices — certainly a more efficient and focused sample