Center for Business Research Working Paper W95-106-94, St. Cloud State University, Minnesota.

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**Abstract:** BACKGROUND:
In 1938, Frank Benford published a paper which described a
numerical phenomena which has come to be known as Benford's Law.
In that paper, Benford demonstrated that the digits of natural
numbers are distributed in a predictable and specific pattern.
For example, if one opened his/her checkbook and determined
how many checks began with 1, 2, 3, etc, one would expect to
find that approximately 30 percent (.30103) of the checks would
begin with 1, 18 percent (.17609) of the checks would begin with
2, 12 percent (.12494) would begin with 3, and so fourth.
Similarly, 0 would be the value of the second digit for
approximately 12 percent (.11968) of the checks, 1 would be the
value of the second digit for approximately 11 percent (.11389)
of the checks, and so on. For a complete explanation of the
derivation of the above table or Benford's Law in general see:
Sundheim and Busta (1993) or Nigrini (1991A, 1991B).
This numeric phenomena has been found to hold with a large
number of data sets (Sundheim and Busta 1993; Burke and Kincanon
1991; Sentance 1973; Varian 1972; Wlodarski 1971). Street
addresses, death rates, areas of rivers, population of cities
Benford 1938), accounting measures of net income (Carslaw 1988;
Thomas 1989), and dollar amounts on utilities bills are a few of
the sets of numbers which have digits which are closely
distributed in accordance with Benford's Law. Busta and
Sundheim (1992) have discovered that tax return data follow a
Benford distribution.
Additionally, several researchers (Hill 1988; Neuringer
1986; Chernoff 1981; Tune 1964; Bakan 1960; Chapanis 1953) have
empirically determined that when individuals manufacture numbers
"from their heads," that the numbers do not follow a Benford
set. This important empirical discovery, coupled with the fact
that tax return numbers follow a Benford set (Busta and Sundheim
1992) provide the theoretical foundation for the concept that
Benford's Law could be used to detect manipulated tax returns.
Consequently, the purpose of this paper is to determine if
tax returns which contain manufactured numbers (manipulated tax
returns) deviate more from Benford's law, than tax returns which
do not contain manufactured numbers (non-manipulated tax
returns)

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**Reference Type:** E-Print

**Subject Area(s):** Accounting