Zeroing in on Fraud

Advanced Statistical Analysis

By Robert Tie


statistical-analysis Fully explaining advanced statistical analysis would require a course-length discussion. But this article's brief description of how such techniques can help deter and detect fraud might lead some CFEs to explore them further. As discussed below, the ACFE soon will offer a new seminar, Data Analysis for Fraud Detection.

Regression analysis — for many, these words provoke anxiety and uncertainty. But fraud examiners with statistical savvy enjoy considerable forensic advantages. Mark Shirley, CFE, CPA/ABV, is one such practitioner.

A principal of V&L Consultants, LLP, of Baton Rouge, La., Shirley has always been a hunter. When he was growing up, he tracked pheasant and wild turkey through marsh and woodlands. These days, he stalks deadly predators who destroy businesses and economic value by, for example, falsifying financial statements.

"In some ways, detecting fraud is like pursuing game," Shirley said.



While studying chemistry and physics in college, including coursework in statistics and higher math, Shirley grew interested in business and majored in accounting. After graduation, as a field agent for the U.S. Internal Revenue Service, he investigated tax-shelter abuse, money laundering and securities fraud. In 1984, he left government and became a CPA and ultimately specialized in business valuation and forensic financial analysis. He earned the CFE credential in 2001.

When performing valuations or supporting litigation, Shirley and his partners use advanced statistical techniques to quantify financial losses and expose signs of potential fraud.

"Correlation analysis helps you evaluate the strength of the connection between two or more pieces of information on, for example, a balance sheet or an income statement," Shirley said. "Suppose you find a strong correlation between consulting expenses and earnings over an adequate period of time. You then would use regression analysis to assess any fluctuations that had occurred in that relationship, compared to the historical norm for that organization or its industry. The goal is to find out whether, and if so, when and why the relationship entered a new phase and to isolate any red flags that might warrant a fraud investigation."

Figure 1 below depicts a regression graph. Values above the regression line, such as yi in this example, merit further analysis to determine their natures and causes. Regression's precise focus makes it possible to eliminate from suspicion the vast majority of items, which have a low probability of being fraudulent.



Figure 1, regression graph

Shirley augments such analysis with a useful tactic he learned as a young hunter.

"I look for things that aren't present, but should be," he said. "Sometimes out in the field, a sudden hush will fall over everything as a bear or other large predator approaches. Well before it arrives, smaller creatures recognize that sound and scent. They quiet down and sit tight. But hunters, who can't perceive those signs until much later, must be alert to the unnatural silence. CFEs need that same sensitivity to things that are inappropriately missing from a financial statement or fraud fact pattern. Advanced statistical analysis can provide such awareness. But first you have to learn the basics."





Some misinterpret the findings of advanced statistical analysis as virtual certainties, rather than as the estimates they really are.

"It's imperative to understand what statistical analysis does not tell you," Shirley said. "Findings with a confidence level of 95 percent are not absolute, but some observers and even some analysts seem to think they are. For example, Orange County, California, went bankrupt in 1994 after being told by its investment company there was a 95 percent probability the county would achieve the returns it sought. There also was a five percent chance it would lose everything. And it did — more than a billion dollars. That's what can happen when you misinterpret a likelihood as a virtual certainty."

Any analysis of such events is incomplete if it does not determine how and why organizations make bad investments or adopt inappropriate strategies.

"You do that by picking apart the financial statements and other documentation on which an organization based its investment decisions," Shirley said. "Using advanced statistical analysis, you can determine whether its assumptions make financial sense. If they don't, your next step is to examine the relationship between those who made the deal to see whether there were any conflicts of interest or other improprieties that would warrant investigation. Your prior analysis puts you in a stronger investigative position than if you had promptly launched a witch hunt before eliminating other possible reasons for that failed investment strategy."


While it is futile to expect absolute answers from statistical analysis, it is important to mitigate factors that can reduce the precision of results.

"When you gather data to analyze, keep in mind that sampling error is the most common cause of misleading or false inferences derived from statistics," Shirley said.

Examples include samples that are too small for extrapolating reasonable estimates about the entire dataset, samples that are arbitrary or biased and samples in which unusual items — known as outliers — are dismissed as irrelevant or too atypical to warrant analysis.

"When fraudsters compare the risk and reward of executing a lucrative phony transaction, they're encouraged by the likelihood that deficient audit samples will overlook their fraud," Shirley said. "If the fraudsters own or lead the organization, they might doctor the financial statements and cover their tracks by changing their accounting firm every few years. Then, any auditor that reviews only the past two years' financial statements would miss, for example, a fraudulent misappropriation of assets that five years ago abruptly disappeared from the balance sheet without explanation. That's why, when analyzing an organization's books, I look at 10 years of daily operations, which can involve millions of pieces of data. Because today's storage is speedy and almost unlimited, we can mine that data quickly. So, I make a point of getting all there is."


Once Shirley has gathered his sample and scanned it for missing data or other suspicious anomalies, he puts his eyes to work in another way — with a scatter plot as depicted in figure 2.



Figure 2, scatter plot

"Often, we can learn more from what we see than what we read," Shirley said. "As I progress from a correlation analysis to regression, a scatter plot enables me to see the data not just as numerical values, but as points whose relationships and dispersion I can interpret visually. In many cases, this gives me more information than a mathematical equation does about how one group of data elements influences another over time. That's particularly valuable in detecting suspicious events and transactions."


"These statistical tools make it easier to incisively evaluate even large quantities of financial data in all their dimensions and relations," Shirley said. "And you don't need advanced software to perform these calculations; an electronic spreadsheet is adequate. Once you've learned how to perform statistical analysis, keep at it. Your skills are like muscles — use them, and they grow; don't, and they atrophy."


In March 2012, the ACFE will hold the first session of its new course, Data Analysis for Fraud Detection. Information on registration will be available soon.

Robert Tie is a New York business writer. 


 The Association of Certified Fraud Examiners assumes sole copyright of any article published on or ACFE follows a policy of exclusive publication. Permission of the publisher is required before an article can be copied or reproduced. Requests for reprinting an article in any form must be emailed to