Page 372 - JoFA_2022

Authentic journal entries with added
Benford’s Law proportion and the actual propor-
fictitious amounts
tion are almost equal. The conformity of the data to
Benford’s Law can be measured by calculating the
average of all the deviations (the spikes above the Part 1: Added fictitious journal entries $2,000–$4,999
Benford’s Law line and the gaps below the Ben-
0.05
ford’s Law line). By this metric (called the mean
absolute deviation) the conformity level is a little Valley Ridge Valley
better (the deviations or differences are slightly
0.04
smaller) than what I’ve usually seen in populations
Benford's Law
of corporate journal entries.
I chose to analyze the first-two digits, even
though Benford’s Law is usually associated with 0.03
the first digits of the amounts in tabulated data. I PROPORTION
did this because of the bluntness issue associated 0.02
with the first digits and for reasons related to audit
efficiency. First, individuals can fictitiously increase
the dollar amount of a valid journal entry (impact-
0.01
ing accuracy) by a reasonably large percentage
that leaves the first digit unchanged. For example,
$1,510, $2,204, and $3,100 can all be increased by
0.00
28.5%, and the new inflated amounts will still have
10 20 30 40 50 60 70 80 90
first digits of 1, 2, and 3, respectively. Second, a FIRST-TWO DIGITS
first-digit test will give audit samples that are large
and inefficient. In the figure “The First Two-Digits Part 2: Added more fictitious journal entries $2,000–$4,999
of the Population of Journal Entries,” the first digit
5 amounts (with first-two digits from 50 through 0.05
to 59) are significantly overstated, and testing all
Valley Ridge Valley
the first digit 5 amounts would mean testing 8.9%
of the population. The first digit 5 over is almost 0.04
entirely explained by the spike (the excess) at 50, Benford's Law
and testing the first-two digit 50 amounts would
mean testing only 2% of the population, a marked 0.03
reduction in audit work. PROPORTION
As the next step in simulating the Health-
South fraud method, I added fictitious journal 0.02
entries, all with dollar amounts from $2,000
to $4,999, to the authentic data shown in the
figure “The First-Two Digits of the Population of 0.01
Journal Entries.” I chose these amounts because
the fictitious entries in the HealthSouth fraud
were all below $5,000, as the CFO knew that 0.00
10 20 30 40 50 60 70 80 90
the auditors only tested journal entries of $5,000 FIRST-TWO DIGITS
and higher. I assumed that the fictitious entries Source: Mark Nigrini.
were evenly distributed from $2,000 to $4,999
because anything smaller than $2,000 would only added to the authentic journal entries. Part 2 of
have had a small net income impact. The fictitious that figure shows the results after adding still
entries would have been “extra” journal entries, another 49,000 such amounts to the authentic
like the cream floating on top of Irish coffee, with journal entries.
their first-two digits evenly distributed from 20 to The fictitious journal entries inflated the actual
49. Part 1 of the figure “Authentic Journal Entries proportions from 20 to 49 ($2,000 to $4,999). In
With Added Fictitious Amounts” shows the new Part 1 of the figure “Authentic Journal Entries
first-two digits graph after 49,000 amounts (10% With Added Fictitious Amounts,” a ridge has
of the total) ranging from $2,000 to $4,999 were formed from 20 to 50, a ridge being a range in the

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