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Referred to as the First-Digit Law, Benford’s Law is a mathematical theory conceived over 70 years ago that has aided numerous anti-fraud professionals in solving embezzlement, insurance claims and money laundering cases. Benford's Law gives the expected patterns of the digits in unaltered data, and explains there is a large bias towards the lower digits, so much so that nearly one-half of all numbers are expected to start with the digits 1 or 2.

In this webinar, we will explain the theory behind the law and how it can be used to find potential fraud and errors to help turn your internal audit or fraud investigation into a revenue generating center.

In this session, you will learn:

• How to apply Benford’s law analysis to find outliers in processes such as cash disbursement, general ledger, insurance claims, tax assessments, etc.

• The types of data that do and do not conform to Benford’s Law

• A practical guide to apply Benford’s tests using IDEA software (1st digit, 2nd digit testing, advanced analytics – fuzzy logic, etc.)

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- 1. Using Benford’s Law for Fraud Detection & Auditing Rohit Kundu, CAATs Expert July 2014
- 2. • AuditNet® features: • Over 2,000 Reusable Templates, Audit Programs, Questionnaires and Control Matrices • Networking Groups & Online Forums through LinkedIn, Google and Yahoo • Audit Guides, Manuals, and Books on Audit Basics CaseWare Analytics (IDEA) users receive full access to AuditNet templates
- 3. • Founded in 1988 • An industry leader in providing technology solutions for finance, accounting, governance, risk and audit professionals • Over 400,000 users of our technologies across 130 countries and 16 languages • Customers include Fortune 500 and Global 500 companies • Microsoft Gold Certified Partner CaseWare International
- 4. International Acceptance
- 5. • What is Benford’s Law? • Conforming/Non-Conforming Data Types • Practical Applications of Benford’s Law • Major Digit Tests • Demo • Q&A Agenda
- 6. Timeline 1881- Simon Newcomb 1938 – Frank Benford 1961 - Roger Pinkham 1992 - Mark Nigrini From Theory to Application Simon Newcomb’s Theory: 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.” Pg. 40. American Journal of Mathematics, The Johns Hopkins University Press
- 7. Timeline 1881- Simon Newcomb 1938 – Frank Benford 1961 - Roger Pinkham 1992 - Mark Nigrini From Theory to Application Frank Benford: • Analyzed 20,229 sets of numbers, including, areas of rivers, baseball averages, atomic weights of atoms, electricity bills, etc. Conclusion Multi digit numbers beginning with 1, 2 or 3 appear more frequently than multi digit numbers beginning with 4, 5, 6, etc.
- 8. Timeline 1881- Simon Newcomb 1938 – Frank Benford 1961 - Roger Pinkham 1992 - Mark Nigrini From Theory to Application Data 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%
- 9. Timeline 1881- Simon Newcomb 1938 – Frank Benford 1961 - Roger Pinkham 1992 - Mark Nigrini From Theory to Application 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.
- 10. 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 Benford’s Law
- 11. 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.
- 12. Benford’s Law Defined
- 13. Conforming 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…
- 14. Conforming Data Types - Examples • 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.
- 15. Non-Conforming Data Types • Data where pre-arranged, artificial limits or nos. influenced by human thought exist i.e. built-in maximum or minimum 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.
- 16. Usage of Benford’s Law • Within a comprehensive Anti-Fraud Program COSO Framework Risk Assessment Control Environment Control Activities Information and Communication Specify organizational objectives Monitoring
- 17. High- Level Usage of Benford’s Law • Risk-Based Audits – Planning Phase 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.
- 18. High- Level Usage of Benford’s Law • 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
- 19. Major Digit Tests (using IDEA) • 1st Digit Test • 2nd Digit Test • First two digits • First three digits • Last two digits • Second Order Test
- 20. 1st & 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
- 21. First Two Digits Test • More focused and examines the frequency of the 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 -- > 2600 invoices -- > (1.78% + 1.69%) x 10,000 -- > (178 + 169) = 347 invoices Only examine invoices beginning with the first two digits 31 and 33. Source: Using Benford’s Law to Detect Fraud , ACFE
- 22. First Three Digits Test • Highly Focused • Used to select audit samples • Tends to identify number duplication
- 23. Last Two Digits Test • Used to identify invented (overused) and rounded numbers • It is expected that the 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 the time. Source: Fraud and Fraud Detection: A Data Analytics Approach, John Wiley & Sons, Inc., Hoboken, New Jersey
- 24. Second Order Test • Based on the 1st two digits in the data. • A numeric field is sorted from the smallest to largest (ordered) and the 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
- 25. Continuous Monitoring Framework • Automated & Repeatable Analysis • Input New Analytics with Ease • Remediation Workflow & Resolution Guidelines • KPIs (Root Cause Analysis)
- 26. Continuous Monitoring Framework Turn-key Solutions • P2P • Purchasing Cards and T&E Monitoring – Identify transaction policy violations – Spend, Expense & Vendor profiling – Identify card issuance processing errors – Evaluate trends for operational/process improvements
- 27. Conclusion Benford’s Law • 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 us a better understanding of our data • Need to use Benford’s Law together with other drill down tests • Technology enables this faster and easier to produce results
- 28. Rohit Kundu Rohit.kundu@caseware.com Sunder Gee Sunder.Gee@ZapConsulting.ca IDEA Inquiries salesidea@caseware.com Q & A

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