Tag: fraud

Benford’s Law and Fraud Detection

Civil fraud cases hinge on litigants proving where specific fraudulent activity occurred. Tax returns, sales records, expense reports, or any other large financial data set can be manipulated. In many instances of fraud, the accused party diverts funds or creates transactions, intending to make their fraud appear as ordinary or random entries. More clever fraudsters ensure no values are duplicated or input highly specific dollar and cent amounts. Such ‘random’ numbers, to them, may appear normal, but few understand or replicate the natural distribution of numbers known as Benford’s Law.

A staple of forensic accounting, Benford’s Law is a useful tool for litigants in establishing patterns of fraudulent activity.

Benford’s Law states that, for any data set of numbers, the number 1 will be the leading numeral about 30% of the time, the number 2 will be the leading numeral about 18% of the time, and each subsequent number (3-9) will be a leading number with decreasing frequency.  This decreasing frequency of numbers, from 1 though 9, can be represented by a curve that looks like this:

Frequency of each leading digit predicted by Benford’s Law.

For example, according to Benford’s Law, one would expect that more street addresses start with a 1 than a 8 or 3; such hypothesis can be tested and proven. The same pattern holds for any number of phenomenon: country populations, telephone numbers, passengers on a plane, or the volumes of trades. This predicted distribution permeates many aspects of numbers and big data sets. But Benford’s Law is not absolute: it does require larger data sets, and that all the leading digits (1-9) must have a theoretically equal chance of being the leading digit. Benford’s Law, for example, would not apply to a data set where only 4s or 9s are the leading number. Financial data sets do comport with a Benford distribution.

In accounting and financial auditing, Benford’s Law is used to test a data set’s authenticity. False transaction data is typically tampered by changing values or adding additional fake data. The test, therefore, is an early indicator if a data set has been altered or artificially created. Computer generated random numbers will tend to show an equal distribution of leading digits. Even manually created false entries will tend to have some sort of underlying pattern. A person may, for example, input more fake leading digits based on numbers closer to their typing fingers (5 and 6).

An examiner would compare the distribution of leading digits in the data set, and the Benford distrubtion. Then, the examiner would statistically test if the proportion of leading numbers in the data set matches a Benford distribution. The resulting “Z-scores” give a measure of how distorted these distributions are, with higher “Z-scores” implying a more distorted data set, which implies artificially created data.

If a data set violates Benford’s Law, that alone does not prove such transactions numbers fraudulent. But, a violation does give auditors, economists, and fact finders an additional reason to scrutinize individual transactions.

Data Analytics and the Law: Putting it Together

This series on data analytics in litigation emphasized how best practices help secure reliable, valid, and defensible results based off of “Big Data.” Whether it is inter-corporate litigation, class actions, or whistleblower cases, electronic data is a source of key insights. Courts hold wide discretion in admitting statistical evidence, which is why opposing expert witnesses scrutinize or defend results so rigorously. There is generally accepted knowledge on the techniques, models, and coding languages for generating analytical results from “Big Data.” However, the underlying assumptions of a data analysis are biased. These assumptions are largest potential source of error, leading parties to confuse, generalize, or even misrepresent their results. Litigants need to be aware of and challenge such underlying assumptions, especially in their own data-driven evidence.

 

When it comes to big data cases, the parties and their expert witnesses should be readily prepared with continuous probing questions. Where (and on what program) are the data stored, how they are interconnected, and how “clean” they are, directly impact the final analysis. These stages can be overlooked, leading parties to miss key variables or spend additional time cleaning up fragmented data sets. When the data are available, litigants should not miss on opportunities due to lack of preparation or foresight. When data do not exist or they do not support a given assertion, a party should readily examine its next best alternative.

 

When the proper analysis is compiled and presented, the litigating parties must remind the court of the big picture: how the analysis directly relates to the case. Do the results prove a consistent pattern of “deviation” from a given norm? In other instances, an analysis referencing monetary values can serve as a party’s anchor for calculating damages.

 

In Big Data cases, the data should be used to reveal facts, rather than be molded to fit assertions.

Data Analytics and the Law: Analysis

For data-based evidence, the analysis is the heart of the content: the output of the data compiled for a case. In most instances, the analytics do not need to be complex. Indeed, powerful results can be derived by simply calculating summary statistics (mean, median, standard deviation). More complicated techniques, like regressions, time-series models, and pattern analyses, do require a background in statistics and coding languages. But even the most robust results are ineffective if an opposing witness successfully argues they are immaterial to the case. Whether simple or complex, litigants and expert witnesses should ensure an analysis is both relevant and robust against criticism.

 

What type of result would provide evidence of a party’s assertion? The admissibility and validity of statistical evidence varies by jurisdiction. In general, data-based evidence should be as straightforward as possible; more complex models should only be used when necessary. Superfluous analytics are distractions, leading to expert witnesses “boiling the ocean” in search of additional evidence. Additionally, courts still approach statistical techniques with some skepticism, despite their acceptance in other fields.

 

If more complex techniques are necessary, like regressions, litigants must be confident in their methods. For example, what kind of regression will be used? Which variables are “relevant” as inputs? What is the output, and how does it relate to a party’s assertion of fact? Parties need to link outputs, big or small, to a “therefore” moment: “the analysis gave us a result, therefore it is proof of our assertion in the following ways.” Importantly, this refocuses the judge or jury’s attention to the relevance of the output, rather than its complex derivation.

 

Does the analysis match the scope of the complaint or a fact in dispute? Is the certified class all employees, or just a subset of in a company? Is the location a state, or a county within a state? If the defendant is accused of committing fraud, for how many years? Generalizing from a smaller or tangential analysis is inherently risky, and an easy target for opposing witnesses. If given a choice, avoid conjecture. Do not assume that an analysis in one area, for one class, or for one time automatically applies to another.

 

A key component of analytical and statistical work is replicability. In fields such as finance, insurance, or large scale employment cases, the analysis of both parties should be replicable. Outside parties should be able to analyze the same data and obtain the same results. In addition, replicability can expose error, slights of hand, or outright manipulation.

 

Data-based evidence requires focus, clarity, and appropriate analytical techniques, otherwise an output is just another number.

Data Analytics and the Law: Unstructured Data

Data analytics is only beginning to tap into the unstructured data which forms the bulk of everyday life. Text messages, emails, maps, audio files, PDF files, pictures, blog posts, these sources represent ‘unstructured data,’ as opposed to the structured data sources mentioned thus far. Up to 80% of all enterprise data is unstructured. So, how can a client’s text messages or recorded phone calls be analyzed like a SQL table? Unstructured data is not easily stored into pre-defined models or schema; some CRM tools (e.x. Salesforce) do store text-based fields. But typically, documents do not lend themselves to traditional queries from a database. This does not mean ‘structured’ and ‘unstructured’ data are in conflict with each other.

 

Document based evidence is of course, an integral part of the legal system. Lawyers and law offices now have access to comprehensive e-discovery programs, which sift through millions of documents based on keywords and terms. Selecting relevant information to prove a case is nothing new. The intersection with Data Analytics arises when hundreds of thousands or millions of text based data are analyzed as a whole, to prove an assertion in court.

 

Turning unstructured text into analyzable, structured data is made possible by increasingly sophisticated methods. Some machine learning algorithms, for example, analyze pictures and pick up on repeating patterns. Text mining programs scrape PDFs, websites, and social media for content, and then download the text into preassigned columns and variables. Analyses can be run, for example, on the positivity or negativity of a sentence, the frequency of certain words, or the correlation of certain phrases to one another. Natural language processing (NLP) includes speech recognition, which itself has seen significant progress in the past two decades. Analytics on unstructured data is now more useful in producing relevant evidence.

 

As important as the unstructured data is its corresponding Metadata: data that describes data. A text message or email contains additional information about itself: for example the author, the recipient, the time, and the length of the message. These bits of information can be stored in a structured data set, without any reference to the original content, and then analyzed. For example, a company has metadata on electronic documents at specific points in a transaction’s life-cycle; running a pattern analysis on this metadata could identify whether or not certain documents were made, altered, or destroyed after an event.

 

In instances of high profile fraud, such as the London Inter-bank Offered Rate (LIBOR) manipulation scandal, prolific emails and text messages between traders added a new dimension to the regulator’s cases against major banks. Overwhelming and repeated textual evidence, which can be produced through analyses on unstructured data, is yet another tool for litigating parties to prove a pattern of misconduct.

Data Analytics and the Law: The Big Picture

With businesses and government now firmly reliant on electronic data for their regular operations, litigants are increasingly presenting data-driven analyses to support their assertions of fact in court. This application of Data Analytics, the ability to draw insights from large data sources, is helping courts answer a variety of questions. For example, can a party establish a pattern of wrongdoing based on past transactions? Such evidence is particularly important in litigation involving large volumes of data: business disputes, class actions, fraud, and whistleblower cases. The use cases for data based evidence increasingly cuts across industries, whether its financial services, education, healthcare, or manufacturing.  

 

Given the increasing importance of Big Data and Data Analytics, parties with a greater understanding of data-based evidence have an advantage. Statistical analyses of data can provide judges and juries with information that otherwise would not be known. Electronic data hosted by a party is discoverable, data is impartial (in the abstract), and large data sets can be readily analyzed with increasingly sophisticated techniques. Data based evidence, effectively paired with witness testimony, strengthens a party’s assertion of the facts. Realizing this, litigants engage expert witness to provide dueling tabulations or interpretations of data at trial. As a result, US case law on data based evidence is still evolving. Judges and juries are making important decisions based the validity and correctness of complex and at times contradictory analyses.

 

This series will discuss best practices in applying analytical techniques to complex legal cases, while focusing on important questions which must be answered along the way. Everything, from acquiring data, to preparing an analysis, to running statistical tests, to presenting results, carries huge consequences for the applicability of data based evidence. In cases where both parties employ expert witnesses to analyze thousands if not millions of records, a party’s assertions of fact are easily undermined if their analysis is deemed less relevant or inappropriate. Outcomes may turn on the statistical significance of a result, the relevance of a prior analysis to a certain class, the importance of excluded data, or the rigor of an anomaly detection algorithm. At worst, expert testimony can be dismissed.

 

Many errors in data based evidence, at their heart, are faulty assumptions on what the data can prove. Lawyers and clients may overestimate the relevance of their supporting analysis, or mold data (and assumptions) to fit certain facts. Litigating parties and witnesses must constantly ensure data-driven evidence is grounded on best practices, while addressing the matter at hand. Data analytics is a powerful tool, and is only as good as the user.