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

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.

9. BENFORD’S LAW DEFINED

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 salesidea@caseware.com to
schedule a demonstration

25. USING BENFORD’S LAW FOR FRAUD
DETECTION & AUDITING
Visit casewareanalytics.com
Email salesidea@caseware.com