Fraud Detection: Using (and Graphing) Benford's Law

Arbutus Analyzer can assist in quickly and efficiently detecting fraud in a number of ways. One of Analyzer’s methods of fraud detection is called Benford’s Law – also referred to as first-digit distribution law. This type of analysis looks at the distribution leading digits of a set of numbers and compares it to statistical findings that govern how often these leading digits should occur in random number sets. Results that feature major discrepancies between your data set and Benford’s Law norms indicate that your organization should take a second look at the data that falls out of place. Variance from Benford’s Law should be examined to determine if someone is bypassing controls or manipulating thresholds.

To demonstrate Benford’s Law analysis, I have downloaded a data set from the website (a website that tracks Australian Government procurement greater than $10,000). The Benford’s Law analysis will be applied to the Value_AUD field, which reports the dollar amount spent by various government departments in the procurement of certain items.

First, select the column to which you wish to apply your analysis – in this case the Value_AUD column.  Looking at the top horizontal menu, click Analyze, and then Benford.

The pop-up menu that appears provides you the option to check the Benford key field you are applying the analysis to, as well as specify the number of leading digits the analysis will be performed on (in this case I have selected 1, signifying I only want to analyse the distribution of the first digit in a number string).

Clicking More >> reveals further tabs where you can request Output options – “Screen” will formulate a numerical table comparing the actual count to the expected count of leading digits, whereas “Graph” will form a graph for a more visual and often easier to understand output. “Data” will produce the Benford’s Screen results in a new data file which can be manipulated with further commands.

For the purposes of this demonstration I have selected “Graph,” which I often find is the easiest to understand and will give me a quick visual snapshot of my data.

The graph looks like the following. The pink line indicates the expected distribution of leading digits, and the blue bars indicate where leading digits in your data actually fall.

From the graph in this particular example, it is seen that the leading digit in the amount spent across my data set is fairly consistent with a Benford number distribution. This provides the reader some comfort that procurement officers are not manipulating the dollar value of tenders as (for this set) the price was reasonably aligned with Benford’s Law.

Changing graph properties is simple – looking at the menu running vertically down on the left-hand side on the graph tab, it is possible to customize graph type (in Benford’s Law graphs, the options are bars as displayed above or lines only), graph properties (font, background and frame), and legend and axis properties. Further down there are also options that allow you to copy your graph to the clipboard, save your graph as a bitmap file, or print your graph.

Below I have edited some of these customizations.

In this example I removed all legend and axis titles and all other titles and frames to create a simple, minimalist graph. I also made the background white so it would fit transparently onto a white document.

In this example I selected the graph type to be lines only, thereby allowing me to see more precisely where the discrepancies between the actual and expected counts lie.

To summarize: Benford’s Law is a quick and easy way to help detect potential fraud.

To execute:

  • Select the Analyze menu

  • Look for “Benford” in the drop down menu

  • Choose column, number of leading digits to analyze, and output type

  • Select OK

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