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FRAUD / AUDITING

The first-two digits of the invoice amounts data analytics will be at detecting a below-the-
testing-threshold fraud scheme, provided that the
follow-up audit work is done competently.
BENFORD’S LAW-BASED AUDIT PLANNING
AU-C Section 315, Understanding the Entity and
Its Environment and Assessing the Risks of Material
Misstatement, requires auditors to identify journal
entries that might represent specific risks, including
unusual transactions, events, amounts, ratios, and
trends. Benford’s Law-based audit analytics can also
be used to identify unusual transactions in journal
entries, as I demonstrate in the following example.
The data I used is a file of invoices processed
for payment by an electricity supply company over
a 16-month period. The file was made available to
me for in-house training and for research purposes.
There were 189,470 invoices processed for payment
for a total of $490,277,625. About one-half of the
total dollars went to pay the 370 invoices for invoice
Source: Mark Nigrini.
amounts of $100,000 and higher. The first-two dig-
its of the invoice amounts are shown in the figure
The first-two digits of the invoice amounts “The First-Two Digits of the Invoice Amounts.”
with a threshold line Note that in this figure there is an extreme
spike at 50, together with two noticeable twin
spikes (overs), at 10 and 11, and at 98 and 99. In
this application, I wanted to identify a selection
of the largest spikes that would become actionable
(or notable) spikes (spikes that an auditor should
investigate).
To help with this selection I added a threshold
line to the graph (see the figure “The First-Two
Digits of the Invoice Amounts With a Threshold
Line”) above which a spike is statistically signifi-
cant. For large datasets, setting a threshold line
based on statistical significance will make it too
tight (too close to the Benford’s Law line) to be
practical. My recent experience with journal entry
populations has shown that fixing the threshold line
based on an audit population of 2,000 records gives
an ideal balance between doing too little audit work
and missing potential irregularities and doing too
Source: Mark Nigrini. much audit work chasing false positives. I therefore
set the threshold line loosely based on statistical
significance with a lenient adjustment upward
and the mean absolute deviations of the graphs in because we expect accounting data to only closely
the figure “Authentic Journal Entries With Added approximate, as opposed to perfectly conform to,
Fictitious Amounts” are significantly higher than Benford’s Law.
those of the authentic data. In a separate, unpublished analysis, I found that
The tighter the range ($2,000 to $4,999 in the there was only a small chance that a spike caused by
simulations) of the fictitious entries, and the larger random variation in the data would peak above the
the percentage of fictitious entries in the popula- threshold line. The result is that spikes above the
tion, the more effective Benford’s Law-based audit threshold line are caused either by an irregularity

18 | Journal of Accountancy September 2022