Benford’s Law Practical Application

Introduction :
Now a days as we all know importance and use of automated software for
accounting as well as for record keeping has been increased. Risk factor
also has challenging role while conducting the audit in automated
environment. To facilitate these challenges there are already many
theorems are present but the important thing is how far we can use them
while working in audit and assurance field. Out of these theorems one is
Benford’s law which is mainly concerns with numeric indicators related to
manipulation of accounts and records. Benford’s law describes the relative
frequency distribution for leading digits of numbers in datasets. In this
article we are discussing the possible ways to implement this theorem
with understanding our needs and business practices of record keeping.

Facts of Law:- it is an observation that in many real-life sets of numerical data, the
leading digit is likely to be small. Generally In sets that obey the law, the number 1
appears as the leading significant digit about 30% of the time, while 9 appears as
the leading significant digit less than 5% of the time. If the digits were distributed
uniformly, they would each occur about 11.1% of the time.[Wikipedia] Benford’s
law also makes predictions about the distribution of second digits, third digits,
digit combinations, and so on. In short it is the frequency of occurrence of digits at
first or second place in any relevant database as the case may be which is
commonly observed in practice and probability is described by using percentage
which is calculated by using formula = Log10(1+1/n). For calculating of probability
of digit 1 we can put 1 in n’th place and got 30.1% and so on up to 9th digit, the
probability percentage is stated below:-
If N is 1 then=30.1% If 2 then=17.6% If 3 then=12.5% If 4 then=09.7%

If 5 then=07.9% If 6 then=06.7% If 7 then=05.8% If 8 then=05.1% If 9 then=04.6%
So we can calculate percentage of our data say Expenses list etc. by taking first digit of distribution
and if occurrence is different than as above stated percentages then there is possibility of
manipulation. The higher the difference higher is risk of manipulation. Simple comparison of first-
digit frequency distribution from the data with the expected distribution according to Benford’s law
ought to show up any anomalous results [Wikipedia]. One practical use for Benford’s law is fraud
and error detection. It’s expected that a large set of numbers will follow the law, so accountants,
auditors, economists and tax professionals have a benchmark what the normal levels of any
particular number in a set are. Many audit software provides function which calculate deviation so
one can calculate risk of manipulation.

However this law is not always stands true when:- 1. Distributions that would not be expected to obey
Benford’s law 2. Where numbers are assigned sequentially: e.g. cheque numbers, invoice numbers. 3.
Where numbers are influenced by human thought: e.g. prices set by psychological thresholds ($9.99) 4.
Accounts with a large number of firm-specific numbers: e.g. accounts set up to record $100 refunds.
5. Accounts with a built-in minimum or maximum 6. Distributions that do not span an order of magnitude
of numbers. For using this law in excel:- Select the first digit of your distribution by using “left” function.
Here the first digit is first number of 01-04-2021 miscellaneous expenses i.e.3 and for 02-04-2021
its 7 and so on. Then count how many times a single digit is repeated by using “count if” function
and do this for all 1 to 9 digit
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