DIGITAL ANALYSIS IN INTERNAL AUDIT

DIGITAL ANALYSIS IN INTERNAL AUDIT

         Digits can do wonders. Analysis of Digits can do more wonders. It is a methodology  to find abnormal duplications of specific digits, combinations of digits, specific  numbers in corporate data.  Enthusiastic internal auditors and external auditors  may likely to use Digital Analysis which bring value added services to their corporates  and clients. The purpose of this paper submission is to enrich the auditors in the most effective use of digital analysis, based on  Benford’s  Law.

Benfords  Law :

         Similar to the experience of an apple fell on the head of  Sir Isaac Newton,  Frank Benford, a physicist at the GE Research Laboratories  also had a unique experience. In the year, 1920   while at his work spot, Frank Benford noticed that his log table books were more worn at the first few pages than at the last few pages. The first pages give the logarithms of numbers with low first digits. The first digit in a number is the left most digit. For example, the first digit of 1,18,020 is 1 and the third digit is  8. The first and second digit of 7,840 is 7 and 8 respectively. Benford  hypothesized  that he was looking up the logs of numbers with low first digits more often, because there were more numbers with low first digits than with high first digits.

 Origin :

          In 1881, Simon Newcomb, an astronomer and mathematician, published the first known article describing what has become known as Benford’s Law in the American Journal of Mathematics. He observed that library copies of books of logarithms were considerably more damaged  in the starting pages which dealt with low digits and comparitively less damaged on the pages dealing with higher digits. He himself inferred from this pattern that fellow scientists used those tables to look up numbers which started with the numeral one more often than those starting with two, three and so on. The obvious conclusion was that more numbers exist which begin with the numeral one than with the large numbers. Newcomb calculated that the probability that a number has any particular non-zero first digit is:

                  P(d) = Log10(1+1/d)

          Where d is a  number 1..2...3................9... and  P is the probability.

           Using Newcomb’s formula, the probability that the first digit of a number is one is about 30% while the probability of the first digit a nine is only 4.6 percent. The following table shows the expected frequencies for all digits starting from 0 to 9 in each of the first two places in any number.

Expected Frequencies based on Benford’s Law

DIGIT	FIRST PLACE	SECOND PLACE
0	---	0.11968
1	0.30103	0.11389
2	0.17609	0.10882
3	0.12494	0.10433
4	0.09691	0.10031
5	0.07918	0.09668
6	0.06695	0.09337
7	0.05799	0.09035
8	0.05115	0.08757
9	0.04576	0.08500

  

                     In a nutshell, we may say that Benford’s  law is based on a peculiar observation that lower digits appear more frequently than higher digits in data sets. Hitherto,  we focused  on sample, which is now switched over to population!   

           Let us see how this phenomenon applied to Auditing and Accounting.   

Benford’s Law applied to Internal Audit:

            Not all data sets are expected to have the digit frequencies of Benford’s Law: therefore the guidelines for deciding whether a data set would comply are that:

1.   The numbers in the data set should describe the sizes of the elements in the data set;

2.   There should be no built-in maximum or minimum to the numbers. A maximum or minimum that occurs often would cause many numbers to have the digital patterns of the maximum or minimum;

3.   The numbers should not be assigned. Assigned numbers are those given to objects to identify them. Examples are social security, bank account and telephone numbers, and cheque numbers. 

Benford’s  Law gives auditors the expected frequencies of the digits in tabulated data.The premise is that we would expect authentic, and un manipulated data to exhibit these patterns. If a data set does not follow these patterns,  however a few possible reasons exist to explain this phenomenon.

1.   The data set did not meet the three tests noted above, and/or;

2.   The data set includes invented numbers, biased numbers

or errors.

If a data set follows Benford Law, auditors might conclude that the data have passed a reasonableness. This does not mean that all the numbers are correct, but rather that any errors or manipulations were not significant enough to distort the digit patterns. Auditors would still have to combine Digital Analysis with other analytical procedures and possible statistical sampling procedures.

Audit tests:

         The first and second digit tests are used as high level tests of reasonableness. Experience has shown that large accounts payable files have followed Benford’s Law quite closely. Also the extended values of the Inventory follows Benford’s Law closely. The third, more focused test is to verify the frequencies of the first two digits. The formula for the expected first two digit frequencies under Benford’s Law is :

Expected First Two Digit frequency=log(1+1/FTD)

         The fourth, still more focused test is the number duplication test. Here, the frequencies of the actual numbers in the audit data set are tabulated. The list begins with the most frequently occurring number and ends with the least frequently occurring number. Auditors generally direct their attention to

1.   Numbers that have occurred abnormally often relative to

other numbers;

2.   Odd numbers that have occurred abnormally often;

3.   Round numbers that have occurred abnormally often;

Exemptions :

         Some populations of accounting- related data do not conform to a Benford  distribution. For example, assigned numbers such as cheque numbers, purchase order numbers or numbers that are influenced by human thought , for example, the price of a pair of shoes is 199.99 or ATM withdrawals do not follow Benford’s Law. Assigned numbers should follow a uniform distribution rather than a Benford distribution.

     In addition to an auditor’s perception  in determining which populations fit a Benford distribution, there exist some tests that reveal whether or not Benford’s Law applies to a particular data set. Wallace suggests that if the mean of a particular set of numbers is larger than the median and the skewness value is positive, the data set likely follows a Benford distribution. It follows that the larger the ratio of the mean divided by the median, the more closely the set will follow Benford’s Law. This is true since observations from a Benford distribution have a predominance of small values. The difficulty in relying only on such tests as a screening process, before applying digital analysis, is that if an account contains sufficient bogus observations it could fail the tests; thus, digital analysis would not be applied when, in fact, it should.

Conclusion:

     We conclude that Benford’s analysis, when used correctly, is a useful tool for identifying suspect accounts for further analysis. Because of its usefulness, digital analysis tools based on Benford’s Law are now being included in many popular software packages like ACL and CaseWare 2002.The goal of this paper has been to help auditors more appropriately apply Benford’s law-based analysis to increase their ability to detect ubnormal  transactions or fraud. Benford  analysis is a particularly useful analytical tool because it does not use aggregated data, rather it is conducted on specific accounts using all the data available. It can be very useful in identifying specific accounts for further analysis and investigation.

 References :

1.   Mark J Nigrini  Ph.D, Institute of Internal Auditors

247, Maitland Avenue, Altamonte Sprins, Florida.

2.   “ The effective use of Benford’s Law to assist in detecting fraud in Accounting Data” – M/s Cindy Durtschi, William Hillison & Carl Pacini.  

3.   Chartered Accountant Magazine November 2011 issue.