Simple random sampling in a wage and hour case

An article you may find useful:

http://knol.google.com/k/dwight-steward/simple-random-sampling/15hmam9ln4cjr/5#

Salary discrimination allegations and data

In contrast to cases involving hiring discrimination, employment cases involving discriminatory salary allegations tend to present relatively few special data issues for the statistical expert. Generally, employers tend to keep data records on compensation issues that are sufficient for most statistical employment analyses. In these types of cases, the statistical expert will generally be most concerned with the specification of the underlying compensation process.

For example, in many of the cases both the plaintiff and defendant statistical experts will utilize the same employer salary and generally use the same class of statistical methodologies. The differences between the opposing statistical experts opinions frequently revolves around the specification of the compensation model and the employment actors included in the model.

Hiring discrimination and data

Similar to cases involving discriminatory pay allegations, discriminatory employment termination type cases present relatively few data related issues for the statistical expert. Like pay cases, most of the differences revolve around the specification of the statistical model of the employer’s practices. However, determining which protected and non-protected group members were actually eligible for a given reduction in force action does tend to produce differing opinions

Statistics Saturday: Wage and Hour Statistics Tools

Sampling Error, n. the difference between the
true, and generally unknown, value of a statistic,
such as the mean average salary, of a parent
population and the value that is estimated from a
sample.

Discussion:

Sampling error in commonly presented in national
surveys. For instance, a survey may report that
27%, with a sampling error of +/-3.5%, of the
employees were interested in applying for a given
job.

The sampling error in this example would
mean that it can be expected that had the entire
population been asked the question, between
23.5% and 30.5% of the employees would have
reported that they were interested in the job in
question.

Our damages paper makes the top 10 downloaded list in August!

Our paper entitled, "Back Pay and Front Pay Calculations in Employment Termination Cases: Accounting for Re-Employment and Mitigation Efforts" was recently listed on SSRN's Top Ten download list for

EBCPL: Compensation Law (Topic),
EBCPL: Employee Benefits Law (Topic),
EBCPL: Pension Law (Topic) and EPELL: Theoretical Perspectives on Employment & Labor Law (Topic).

Discriminatory hiring allegations: Special Concerns

Statistical analyses involving hiring allegations tend to present a number of special issues. First, it is not uncommon for organizations to keep only cursory records on individuals who apply for a given job position. Consequently, special attention must be dedicated to the construction of the relevant applicant pool in these types of employment cases. In some instances in hiring analyses, the employer level hiring data is augmented with labor market availability information from government and other publicly available sources to provide a more probative analysis.

Second, in addition to the data issues in hiring cases, the definition of the relevant pool of qualified applicants is typically an issue of concern for the statistical expert. Generally speaking, it is important for the expert to ensure that the hiring analysis compares individuals who, but for their protected class status, would have a comparable probability of being hired. For example, in a case involving allegations of gender discrimination in faculty hiring at a university, factors such as the individual’s prior research and teaching experience would be factors to potentially consider in the construction of the qualified applicant pool.

Third, it is important to consider each of the stages that comprise a typical employer’s hiring process as well as the different factors that may effect the individual’s decisions at each stage of the hiring process. For example, many employers’ hiring processes are comprised of distinct stages that may include the application stage, interview stage, testing stage, and ultimately the selection stage. It is important to clearly define the hiring stages, as well as to determine the number of applicants in both the protected and non-protected group who are not only qualified but are truly interested, potential job candidates for the given position.

Household production and age

Once criticism that economists typically encounter when calculating the loss of household services is that it is unrealistic to use the average number of hours spent on household services because the number of hours that a person will spend performing household services will decrease as the person ages.

Data on the how people allocated their time within a given day (time use surveys) suggest that this criticism is unfounded. For instance, according to time use data from the U.S. BLS the opposite is true. That is the amount of time spent performing household services such as housework, food cooking, outdoor chores, home maintenance, and time spent obtaining goods and services actually increases as a person ages. For example, a male who is between 25 and 34 will spend 11.7 hours performing household services; where as a male between the ages of 65 and 74 will spend 21.3 hours performing household services.

Using statistical evidence in employment cases (Part III)

(2) after accounting for relevant employment factors, does the individual’s protected class status remain a statistically important factor?

This question is typically used by the statistical expert when assessing the importance of the employee’s protected group status in the selection or pay process when there are observable employment related differences among the individuals being analyzed. For instance, it is generally recognized that an individual employee’s salary will tend to be related to factors such as the type of job performed, seniority, education, as well as company specific factors such as time in salary grade.

In these types of discrimination analyses, the expert will develop statistical models, such as linear regression models, to account for the effect that these employment factors and the protected group status collectively have on the selection or compensation process. In these types of models, a finding that the individual’s protected group member status remains a statistically important factor even after accounting for the observable employment related differences among the individuals, is typically viewed as suggestive of a nonneutral employment process.

Spinal Cord Injury and Economic Damages

Each year about 11,000 people in the United States suffer severe but non-fatal injuries to their spinal cords that leave them with some degree of paralysis or loss of motor function. There are now about a quarter of a million people in this country living with spinal cord injuries. Many of these injured parties bring lawsuits alleging negligence or malfeasance and seeking compensation for lost earning capacity and medical costs.

Below is information that should be useful to attorneys trying such cases.

Degrees of spinal cord injury. The location and extent of the injury to the spine determine the degree of loss of body function and have a great impact on the ultimate economic damages for your client. About 53 percent of permanent spinal cord injuries (excluding the small percentage of those who recover) result in paraplegia, or the loss of feeling and movement in the lower parts of the body.

If your client has this type of injury, a vocational rehabilitation expert is likely to find that your client has significant residual earning capacity, perhaps with retraining. The remaining 47 percent suffer from quadriplegia or tetraplegia. Injuries to the top of the spine, vertabra C-1 to C-4, are classified as high tetraplegia and result in paralysis from the neck down while those occurring in vertebra C-5 to C-8 are termed low tetraplegia and result in paralysis from the shoulders down.

Within these categories, paralysis can be complete or incomplete. The most severe non-fatal spinal cord injuries leave a person dependent upon a ventilator while the least severe, resulting in “incomplete motor function,” are evidenced by involuntary movements such as spasms, twitching, and shaking.

Reduced earning capacity. Estimates of how much a spinal cord injury has reduced the capacity of your client to earn income must consider not only pre-injury earning histories but also prospects for post-injury employment. The severity of the injury will obviously determine the feasibility of reemployment and a vocational rehabilitation expert will be needed to evaluate employability in each particular case. The National Spinal Cord Injury Association reports that eight years after their injuries 34 percent of paraplegics and 24 percent of quadriplegics (or tetraplegics) are employed. Many of those who are working have part-time positions and are likely to miss work periodically due to complications from their conditions. Calculations of future earning capacity for your client should be reduced to account for these involuntary breaks in employment and the strong liklihood of a reduced number of remaining years in the workforce.

Medical and living costs. If your client has an extemely severe type of injury, damages for medical care and living costs will probably outweigh damages for lost income. The Spinal Cord Injury Information Network provides “average yearly health care and living expenses that are directly attributable to [spinal cord injuries].” These annual costs, which are highest in the first year after the accident, range from $15,000 to over $700,000, depending upon the severity of the injury. (SCIIN's 2000 dollar values have been inflated to their 2004 dollar equivalents.)

Using statistical evidence in employment cases (Part II)

1) if there was no discrimination against the protected group members, what would be the probability (or sheer random chance) of observing the employment related disparity by random chance alone?

This question is typically used when assessing the statistical importance of an overall difference in selection rates or salary by protected group status. For instance, consider an example where African-American employees earned $10,000 less than similarly situated White employees. In this example, ,the statistical expert will use generally accepted methodologies to calculate the probability that sheer random chance generated the observed racial salary differential between the similarly situated employees.

The probability that is calculated from the expert’s statistical test is commonly referred to as a chance probability.

Consider the situation where the statistical test in the above example determined that there was a chance probability of 1% of observing the racial salary differential between the similarly situated employees. A chance probability in this setting would suggest that if there was NO discrimination against African-American employees, then we would only expect to see the observed racial salary differentials in 1 out of every 100 instances. This finding could be suggestive of discrimination against African-American employees.

A chance probability that is small and equal to or less than a pre-specified threshold is referred to as statistically significant.

Conversely, if the calculated chance probability of observing the racial salary differential was 50%, then we would expect to see the observed employment outcome in 1 out of every 2 instances. Since there is a relatively large chance of observing the employment outcome by random chance, this finding is not suggestive of discrimination against African-American employees.

A chance probability that is large and greater than a pre-specified threshold is referred to as statistically insignificant.

In many court room settings, an employment disparity finding that has less than a 1% chance of occurring by sheer random is viewed as statistically significant. The actual methodology used to calculate the chance probability depends on the type of employment question being addressed by the statistical expert.

Hypothesis testing in employment discrimination cases (part I)

Generally, in an employment discrimination lawsuit, the statistical expert will conduct statistical tests that address one or both of the following employment related questions or hypotheses:

(1) if there was no discrimination against the protected group members, what would be the probability of observing the employment related disparity by random chance alone?

(2) after accounting for relevant employment factors, does the individual’s protected class status remain a statistically important factor?

Declaration design principle #3: Ask the right questions in the right way

(from previous posts)
Once the general focus of the survey or declaration statement is determined, it is
important to make sure that the correct questions are ask of the respondent. The
questions that are asked in the survey should be very focused in nature. The
questions should not be leading, but whenever possible they should be closed end in
nature.

Closed end questions, because they yield a choice based response, allow
the results of the declaration statement to be analyzed in a more quantitative manner.
Furthermore, important issues concerning the wage and hour case should be probed
in a couple of different ways to ensure that all angles of the issue are covered
appropriately. Differently worded questions can yield different responses by potential
class member. When appropriate, the declaration statement document should
include follow-up or check questions that help check the validity of the initial
response.

In the unpaid meal break cases study example above it was important to determine if
the fact that they person did not clock out for a meal break meant that the person did
not actually take a meal break. Anecdotal evidence suggests that many of the
pharmacists took uninterrupted meal breaks but simply did not clock out for the
meals.

Declaration design principle #2: Ask as few questions as possible.

(continued from previous post)

Once the random sample of individuals is selected, the declaration statement or
survey questions must be carefully designed. As a general rule the declaration
statement or survey form, and questions asked of the potential class members,
should be as parsimonious as possible. Shorter forms and questions will tend to
increase the amount of effort and thought that each potential class member puts into
completing the survey.

As a general rule only questions that are germane to the issue at hand should be
included. Questions that ask the respondent about information that can be directly
obtained from other sources, such as human resource or time card records, should
be avoided. For instance, questions that ask about the person’s job title, employment
length or other work schedule related issues should generally be avoided because
this information can be obtained from other sources. The additional work required to
match the respondent's information to the survey responses is generally outweighed
by the benefits of a shorter form.

In the off-the-clock case discussed above, the attorneys, with the assistance of
economists and statisticians, devised a detailed declaration statement document of
the grocery store chain’s pharmacists. The declaration statement document had 10
questions that asked the pharmacists about their meal breaks and the frequency in
which those meal breaks were interrupted. There were also questions about the
individual’s knowledge of the company’s policy concerning meal breaks and their time
clock punch activity.

Declaration statement design principle #1: Use a sampling routine to construct

In many wage and hour class actions, asking only a portion of the individuals to fill
out declaration statements or survey is preferable to obtaining surveys and
declaration statements from every member in the potential class. In many instances,
the potential class members are too geographically dispersed to make a total census
count feasible.

For instance, in the grocery story case study (see previous post) the 700 potential members of the class action worked in over 325 geographically dispersed locations throughout the state.
Most stores had at least one pharmacist on duty 24 hours a day. A total census
count of active pharmacists who would be potential class members would involve
administering a survey over a short period of time to employees spread over 2,800
different work shifts (700 members x 4 shifts). Additional effort would have to be
expended to administer the survey to pharmacists that no longer worked at the
company.

Total census counts, even if they are feasible, may not be desirable because
responses may become contaminated as the declaration statements are collected
from potential class members. It is possible that once word of survey or lawsuit gets
out to all the potential class members, later responses may vary from earlier
responses in non-desirable ways. Individuals who complete a declaration statement
in a wage and hour case after they learn of the lawsuit may subsequently go back
and review pay-stubs or other documents and arrive at the estimate of off-the-clock
work in a different manner from individuals who completed statements earlier. In this
instance, the declaration statements of the later potential class members may be
contaminated and should potentially analyzed in a different manner than the ones
completed earlier.

The bottom line is that even if it were possible to survey every person in a potential
class, you may not want to do so. A well designed sample in a wage and hour class
action will help ameliorate many of the problems associated with attempting to take a
complete census count of the entire potential class.

In the grocery store wage and hour case study, declaration statements were taken
from a random sample of 125 pharmacists across the store’s locations within the
state. The pharmacist sample, which used a technique that is called stratified
random sampling, appropriately reflected the stores located in the northern and
southern part of the state and different shifts that the pharmacist worked.

Declaration Statements and Surveys in Wage and Hour Cases: Part I

A Case Study:

In a recent wage and hour class action, the pharmacists at a major west coast
grocery store chain filed a class action lawsuit in state court that alleged that they
were denied the opportunity to take uninterrupted, duty-free meal breaks. The
pharmacists allege that they were routinely required to answer customer’s questions
and even fill prescriptions during their meal break period. In the state in which the
collective action was filed, the pharmacists were as of January 1, 2001 classified as
non-exempt employees. As non-exempt employees they are entitled to one or two
30-minute duty-free meal breaks depending on the amount of time worked. Across
the state, there are about 700 employees spread over about 325 store locations in
the potential class.

In the lawsuit both the extent and commonality of the off-the-clock wage and hour
violation allegations are at issue. Specially, the defendant’s attorneys are looking to
the use of declaration statements administered to the stores pharmacists to
determine what percentage of the time pharmacists believe their meal breaks were
interrupted by work related duties. In addition, the defense attorneys are looking to
determine how representative the named plaintiffs are of the proposed class of
pharmacists. Finally, the defense attorneys want to know to what degree the
allegations of missed meal breaks vary across the proposed class is also at issue in
this case.

While lawsuits involving missed break are more likely to occur in certain states such
as California which have more defined work and employment laws, and less in
others, the general survey and declaration statement design techniques that are used
in a missed meal break analysis are useful in other types of off-the-clock work cases.
Generally, a survey or declaration statement document that can be used to analyze
wage and hour violation allegations needs to have several main characteristics.

Collecting data in discrimination cases

Regardless of who the attorney is representing, it is important to provide the statistical expert with employment information that completely describes the employment processes that are being studied. Generally this will involve providing the statistical expert not only the hardcopy or electronic employment data that describes the statistical disparity, but in addition, the background information on the employer and the employer’s practices.

Typically, the background information will include information from sources such as electronic databases provided by the defendant, employer handbooks, written descriptions of the relevant selection processes, and depositions of human resource personnel and other key decision makers. If at all possible, engaging the statistical expert early in the discovery process typically will allow the expert to more adequately prepare a listing of the specific information needed in the employment analysis.

In most employment analyses the statistical expert will at a minimum require the following information about the defendant’s employment processes.

A. Employee level information. The employee level information required by the statistical expert includes not only the demographic and employment information, such as date of hire, salary grade, etc., for the plaintiff but also for all the employees in the organization being analyzed. This information will allow the statistical expert to construct comparison pools of ‘similarly situated’ employees.

B. Employer practices information. This type of information includes information about the factors that are incorporated into the employer’s selection or compensation processes. For instance, in cases involving discrimination in employee terminations, it is important to determine the specific formula or individual factors that were considered by the employer in the relevant reduction in force action.

C. Company specific information. This information generally includes company specific factors that describe the organizational differences between different divisions within the relevant analysis unit. For example, in some companies that closely tie financial performance to employee salaries, it is not uncommon to observe higher average pay levels in division that generate higher levels of revenue for the company. For larger organizations, the pay or salary grade structure for the company is also important information for the statistical expert.

S.A.T. scores matter

Economic damage calculations involving minors are tough. One of the major debates concerning calculating losses for minors involves the S.A.T. Simply put some economic experts think the S.A.T. is a strong predictor of future earnings. For examples, some studies, such as http://nces.ed.gov/pubs2000/2000043.pdf, suggest that better performance on the S.A.T. suggest higher earnings in the future.

Some studies have suggested that a 100 point increase in S.A.T. is correlated with a 6 to 10% increase in post-college wages. Other studies, such as the study performed by Daniel Hammermesh et al. in 2002 (They examined the post graduation wages of economics majors) showed either a weakly positive or a statistical unimportant relationship between S.A.T. score and post-graduation earnings. In practical terms, this suggest that the attorney should if the data is available collect information on the S.A.T scores of an injured or deceased minor.

Valuing Stock Options and Stock Purchase Plans

Injury, death, and employment cases frequently involve a plaintiff who has lost out on the value of company stocks that could have been purchased. Generally, the calculation of the number and the amount of company stocks is fairly straightforward. However the value of the lost shares is not as straightforward.

The calculation of the value of the lost shares typically involves the use of sophisticated mathematical models such as the Black-Scholes model. Here are the typical types of plans that the injured or deceased plaintiff could have had:

Employee Stock Option Plans: Stock options plans give the employee the ability to purchase a specific number of shares of a company's stock at a future date at a pre-set price. Options are typically granted for a certain period of time. If individuals do not exercise the options before the end of the period, they expire and are forfeited. Also they must exercise them usually within 3 months of leaving the company. Note that until the individual exercises the option, they are not the owner of the stock.

Employee Stock Purchase Programs: Stock purchase programs give the employee the ability to purchase a quantity of shares of a company’s stock within a certain time period at a discounted price of 10-15%. Employees typically use payroll deduction to purchase stock in a stock purchase program. These purchases must happen within the the allotted time and the individual becomes the owner of the stock at purchase.

Our work in law school

Professor Bales, a law professor at Northen Kentucky University, will use our paper Back Pay and Front Pay Calculations in Employment Termination Cases: Accounting for Re-Employment and Mitigation Efforts in his classes. See his blog review of our work at his , Workplace Prof Blog.

Pensions and Divorce

When valuing a retirement pensions in a divorce case, the idea is to determine the economic value of the pension at the time of divorce. In theory this is done so that the individuals post-divorce work efforts are not incorrectly awarded to the marital period. There appear to be several ways to handle the valuation of a pension in an divorce case.

The ease at which it can be done really depend on if it is a defined benefit or defined contribution plan.

Overall here are the approachs:

1. One approach is to value the defined benefit plan at the date of divorce. In otherwords, just look at what is in the pension at the time of the divorce.

2. Another is to value it at the projected retirement and then to do a time rule analysis, apportioning the pension by the fraction of marital years to total years.

3. A third approach is called here a a QUILDRO qualified Illinois domestic relations order. This approach assigns the pension in proportions in the future. The proportions are based on when the retirement would be paid out.

4. A fourth approach simply values the contributions and their interest as they have been paid in - more appropriate for defined contribution plans. This is somewhat problematic for defined benefit programs.

Stats Saturday: Wage and hour terms to know

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 that are being surveyed.. For
example, in a survey of off-the-clock work,
workers at different locations and different
supervisors may have different work culture
that make it less likely

How long do people work?

The heart of analyzing lost earnings and wages is estimating by how much injury or death decreased a person’s lifetime earning capacity.

This requires estimating how many years the injured or deceased party have otherwise continued working. In many cases, the economist will have to choose some assumption for remaining work life. The simplest assumption is that retirement would come at the age of eligibility for full Social Security benefits. An alternative is to use government data on the median number of years to retirement for workers at any given age and assume that the person would have continued employment for that length of time.

These types of assumptions can be problematic in some settings because they ignore the reality that many people do not conform to these retirement patterns. These analyses ignore the fact that workers at any age have some statistical probability of not being able to continue earning income due to death, physical incapacity, or unemployment. To overcome these difficulties, economists most often use published data that allows them to calculate the average number of remaining years of employment people have at any age.

The Plaintiff Worked for themselves...

Calculating the earnings capacity of individuals who are self employed is involved but very do-able.

The research question in injury and death cases involving the self employed is the same with wage earners: 'How much damage, if any, has been done to the plaintiff's ability to earn a living?'

The biggest difference for the self employed is that there are a number of different ways a self employed person will report the earnings. For instance, some self employed individuals will receive income as an independent contractors while others will receive payments thru a closely held corporation. Other self employed people are sole proprietors; estimating the earnings capacity is different for each of these worker types.

The key piece of information that is used in these analyses is the personal income tax return, usually a form 1040, AND all the supporting schedules. The supporting schedules are used by the analyst to look closer at the plaintiffs' earned wages, business expenses, and to separate accounting adjustments and expenses (such as real estate depreciation) from real business expenses. Attorneys trying to calculate damages in these types of cases should make sure to obtain the supporting tax form schedule for every item on the main 1040 personal tax form . In general, the most accurate estimate of the plaintiffs earnings capacity involves adding reported wages, business income and accounting depreciation.

The Economic Cost of a Life Care Plans

Calculating the economic cost of a life care plan typically involves two steps by economists. First, after figuring out (from the life care plan) what products and services have been prescribed for the injured person, the economist will project the future cost of providing those goods and services at the perscribed times.

For example, what will Prozac cost in 2014? Making this calculation usually means projecting future medical cost using historical medical inflation cost indexes for the services and products in the injured person's life care plan. Second, in some instances the life care plan may call for the economist to make seperate cost projections on the cost of individual items. For instance, there may a service that is not neccessarily medical that the life care planner may ask the economist to value.

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