Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Using Benford's Law for Fraud Detection and Auditing

11,576 views

Published on

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

Published in: Data & Analytics
  • Be the first to comment

Using Benford's Law for Fraud Detection and Auditing

  1. 1. USING BENFORD’S LAW FOR FRAUD DETECTION & AUDITING
  2. 2. AGENDA • What is Benford’s Law? • Conforming/Non-Conforming Data Types • Practical Applications of Benford’s Law • Major Digit Tests
  3. 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. 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. 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. 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. 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. 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.
  9. 9. BENFORD’S LAW DEFINED
  10. 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. 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. 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. 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. 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. 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. 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. 17. USING DATA ANALYTICS (IDEA) • 1st Digit Test • 2nd Digit Test • First two digits • First three digits • Last two digits • Second Order Test
  18. 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. 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. 20. FIRST THREE DIGITS TEST • Highly Focused - Used to select audit samples • Tends to identify number duplication
  21. 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. 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. 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. 24. WANT TO SEE BENFORD’S LAW IN IDEA? Contact us at salesidea@caseware.com to schedule a demonstration
  25. 25. USING BENFORD’S LAW FOR FRAUD DETECTION & AUDITING Visit casewareanalytics.com Email salesidea@caseware.com

×