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.

Often in wage and hour cases, attorneys are faced with the decision of analyzing the complete time and payroll records for a class population, or analyzing just a sample of the population’s records.  While in an ideal world, analyzing the full population of data is the best approach, it may not always be feasible to do so.

For instance, some of the individuals within the class may be missing records due to poor data management, or perhaps both sides agree that the analysis of the full population may be too costly or time consuming.  In these cases, the attorneys can elect to have an expert randomly select a random sample from the full population to perform a reliable and statistically significant random sample.

Below are some common terms related that attorney’s can expect to hear when discussing sampling in their wage and hour cases:

Random Sampling, n. sampling in which every individual has a known probability of being selected.

Sample, n. a set of individuals or items drawn from a parent population.

Sample Size, n. the number of individuals or items in a sample.

Simple Random Sampling, n. sampling in which every individual has an equal probability of being selected and each selection is independent of the others.

Discussion: This very common statistical routine is analogous to ‘pulling a name out of a hat’.

Stratified Sampling, n. a method of statistical sampling that draws sub-samples from different sections, or strata, of the overall data population.

Discussion: Stratified sampling routines are used in employment settings when there are important differences between different groups of employees being surveyed. For example, in a survey of off-the-clock work, workers at different locations, and with different supervisors, may have different work cultures that make them more (or less) likely than other workers to have worked during their lunch period. In this instance, a stratified sampling routine may be used to account for those differences.


The scope of Wage and Hour cases can extend beyond traditional claims on overtime or off-the-clock work. The same analytical principles can extend, for example, to cases involving employee reimbursements. EmployStats is recently worked on a case in California where the Plaintiffs allege they were not reimbursed for routine miles traveled in personal vehicles between job sites, despite the Defendant’s stated policy.

The EmployStats team assessed the Plantiffs’ theory of liability and estimated unreimbursed expenses based off of the available case data on mileage, parking, and toll charges. The analysis presented to the court showed a significant difference between stated and actual reimbursements for miles traveled by the Plantiffs. Based off of the analysis and other evidence at trial, the court certified the Plaintiff class.

The EmployStats Wage and Hour Consulting team’s trial plan is as follows:

  1. First, the EmployStats team would survey a statistically representative sample of class members about the existence of unreimbursed miles, using a random sampling methodology to eliminate potential bias.
  2. Next, the team would use a similar statistical sampling methodology to determine the typical miles traveled by the class members, and combining this resulting data with mapping platforms (ex. Google Maps API) to calculate distances in miles traveled between job locations.
  3. Finally, Employstats would tabulate damages based off of these results, using publicly available data on reimbursement rates for miles traveled in personal vehicles.
A copy of the court’s order can be found though the link here: McLeod v Bank of America Court Order – Dwight Steward PhD Statistical Sampling Plan
To see how EmployStats can assist you with similar employment or statistics cases, please visit or give us a call at 512-476-3711.  Follow our blog and find us on social media! @employstatsnews

On April 5, 2019, Dr. Dwight Steward, Ph.D. will be speaking alongside Robert Cavazos, Ph.D., Kyle Cheek, Ph.D., and Vince McKnight.  The experts and attorney will be presenting together on a panel at the EmployStats sponsored CLE seminar, titled Data Analytics in Complex Litigation.  The seminar will take place at the University of Baltimore in the Merrick School of Business, and will run from 9:30 AM to 1:30 PM.


The speakers will cover a spectrum of issues on Big Data Analytics, and its use in legal applications.  Specifically, the general session of the CLE will provide an overview of data analytics in a legal context, discussing the various aspects of how to manage large data sets in complex litigation settings.  Attendees will then be able to choose between two breakout sessions, Data Analytics in Litigation and Healthcare Litigation.  Lunch will be included.


To find out more on the upcoming CLE, visit:

Also, make sure to follow our blog and stay up to date with Employstats news and sponsored events!

EmployStats is honored to be attending and speaking at the upcoming National Employment Lawyers Association (NELA) Spring Seminar.  The seminar, titled Epic Advocacy: Protecting Wages in Litigation & Arbitration will take place in Denver, CO on April 12-13, 2019.  


EmployStats’ principal economist Dwight Steward, Ph.D., and Matt Rigling, MA, will be presenting alongside attorneys Michael A. Hodgson and Dan Getman.  The speaker’s session, Calculating Damages: Views from an Expert and Lawyers, will discuss all relevant aspects of calculating and proving liability and damages in wage and hour cases.


The panelists will present the options attorneys face when attempting to tabulate damages, discuss the best practices for obtaining and analyzing data, as well as discuss common wage and hour issues such as sampling and surveys.  EmployStats’ statistical experts will also provide statistical background as they relate to labor and employment class action lawsuits, such as a explaining statistical significance, confidence intervals, stratified sampling, and margin of error.


We hope to see you at the upcoming NELA Spring Seminar in Denver on April 13, we would love to meet and discuss how EmployStats can assist you with your wage and hour lawsuit.  To find out more about the seminar, please visit the NELA Website. For more on EmployStats, visit the EmployStats Website.

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.

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.

The Texas Workforce Commission (“TWC”) recently announced they are no longer going to utilize their TRACER 2 application to provide information regarding the Texas labor market.  For many years, the data scientists at EmployStats and other firms in Texas researched economic indicators such as employment statistics, salary and wages, and job growth using the inquiry capabilities of the TRACER 2 application.


The TWC is the state agency responsible for managing and providing workforce development services to employers and potential employees in Texas.  One of the many service the TWC provides is the access for job seekers and data scientists to reliable labor and employment statistics relevant to occupations and industries within the state of Texas.  Specifically, TWC’s TRACER 2 program provided search functions which allowed individuals to freely tabulate market trends and statistics such as employment/unemployment estimates, industry and occupational projections, and occupational wage data within Texas.


With the TWC’s TRACER 2 application “out to pasture” as the TWC puts it, data can now be accessed using a combination of other TWC databases, as well as United States Bureau of Labor Statistics (“BLS”) data such as the Local Area Unemployment Statistics (“LAUS”) and the Current Employment Statistics (“CES”).

A common allegation in wage and hour lawsuits is off-the-clock work.  In these types of cases, employees usually allege that they performed work, such as travel between job sites, that they were not paid for performing.  Other common off-the-clock-work allegations typically involve activities such as spending time in security checkpoints, putting on a uniform, preparing for work, and logging onto computer systems.


Recently, the EmployStats Wage and Hour Consulting team completed work on a case where Plaintiffs alleged unpaid off-the-clock work for time spent driving from their homes to their job sites, as well as travel time between job sites.  In this case, EmployStats was able to analyze and assess Plaintiffs’ allegations by combining and creating datasets of personnel and job location data, and using mapping programs to calculate the time Plaintiffs could have potentially spent traveling and performing off-the-clock work.


The following is an example of how the EmployStats Wage and Hour Consulting team typically handles a case involving travel time:

  1. First, the Employstats team works to combine and merge multiple databases containing employee home locations, employee time and payroll records, and job site locations into a single analyzable database.
  2. The EmployStats team then uses mapping platforms, such as Google Maps API or Mapquest API, to calculate the distance in miles and/or travel time in hours for each unique trip.
  3. Finally, the EmployStats team uses the employee time and payroll records to assess any potential damages due to travel time off-the-clock work.


Check out the EmployStats website to see how we can help you with your wage and hour cases!

After acquiring and merging data, litigants will want to rush to an analysis. But raw datasets, no matter how perfectly constructed, are inevitably riddled with errors. Such errors can potentially bias or invalidate results. Data cleaning, the process which ensures a slice of data is correct, consistent, and usable, is a vital step for any data-based evidence.


There is a often quoted rule in data science which says 80% of one’s time is spent cleaning and manipulating data, while only 20% is spent actually analyzing it. Spelling mistakes, outliers, duplicates, extra spaces, missing values, the list of potential complications is near infinite. Corrections should be recorded at every stage, ideally in scripts of the program being used (ex. R, SAS, SQL, STATA); data cleaning scripts leave behind a structured, defensible record. Different types of data will require different types of cleaning, but a structured approach will produce error free analytical results.


One should start with simple observations. Look at batches of random rows, what values are stored for a given variable, and are these values consistent? Some rows may format phone numbers differently, inconsistently capitalize, or round values. How many values are null, and are there patterns in null entries? Calculate summary statistics for variables, are there obvious mistakes (ex. negative time values)? After an assessment, cleaning can begin.


Fixing structural errors is straightforward: input values with particular spellings, capitalization, split values (ex. data containing ‘N/A’ and ‘Not Available’), or formatting issues (ex. numbers stored as strings rather than integers) can be systematically reformatted. Duplicate observations, common when datasets are merged, can be easily removed.


However, data cleaning is not entirely objective. Reasonable assumptions must be made when handling irrelevant observations, outliers, and missing values. If class X or transaction type Y is excluded from litigation, its reasonable to remove their observations. However, one cannot automatically assume Z, a similar class, can be removed as well. Outliers function the same way. What legal reasoning do I have to remove this value from my dataset? Suspicious measurements are a good excuse; but, just because a value is too big or too small, that alone does not make it reasonable to remove.


Missing data is a difficult problem: how many missing or null values are acceptable for this analysis to still produce robust results? Should you ignore missing values, or should you generate values based off of similar data points? There is no easy answer.  Both approaches assume missing observations are similar to the rest of the dataset. But the fact that the observations are missing data is informative in of itself. A more cautious stance, the one with the least assumptions, will inevitably be easier to defend in court.


Skipping data cleaning, and assuming perfect data, casts doubt on any final product. Data-based evidence follows the maxim “garbage in, garbage out.”