4.5: Defining Populations in Litigation

While there are many fields that have interesting questions about population definition, the field of litigation, particularly when applied to discrimination cases, provides a particularly interesting example of the types of questions that need to be considered when defining a population. While such questions are obviously not relevant to all situations when defining a population, the type of questions considered may be relevant in many other fields.

Discrimination litigation requires specialized experts in both law and statistical procedures. While some of the relevant statistical methodology will be reviewed later, defining the proper population for such studies is crucial. The final arbiter of what the relevant population is for such cases is the judge overseeing the case, and this decision is often made after receiving evidence.

The population used in discrimination litigation can be crucial to the outcome of the case. Lawyers and professional statisticians who specialize in expert witness testimony for these types of cases must be able to help gather evidence in relation to these issues for many potential populations. They must also be able to argue why a specific population should be used over a different choice. As Elaine Shoben, a professor of law who specializes in discrimination cases, stated, “A (statistical) expert's superb analysis on legally irrelevant data is useless” (Shoben 1986).

Discrimination cases often deal with employment and therefore much of the concern is over potential applications to a position. In these cases, a court may decide to compare the pool of applications for a position and compare it to those who were hired. In other cases, a court will compare the general population of all possible applicants versus characteristics of the employer's workforce, or the court will consider the population of potentially qualified applications to a position. This latter case can be used when the job has special qualifications, such as a certification or an advanced degree, or requires certain physical attributes, such as being able to lift a certain amount.

Definition: Applicant Flow

The applicant flow for a position is the collection of individuals who apply for a job or promotion.

A court will often compare the race, gender, ethnicity, and sexual orientation of those in the application flow against those who were hired. Until relatively recently the guidelines for determining if a particular group was discriminated against was based on a rule known as the 80% rule. Using this rule the hiring rate of any group cannot be less than 80% of the rate of another group (Shoben 1986). For example, if employees are classified by gender as female or male, the rate at which females are hired must be at least 80% of the rate at which males are hired. Therefore if 35% of the female applicants are hired and 70% of the male applicants are hired, the hiring rate of female applicants is \(35\div70=0.5\), or 50% of that for male applicants, yielding evidence of discrimination. On the other hand, if 60% of the female applicants are hired and 70% of the male applicants are hired, the hiring rate of female applicants is \(60\div 70=0.86\), or 86% of that for male applicants. In this case these results do not provide evidence of discrimination. This is a controversial and arbitrary measure, and alternative methods have been proposed (Boardman 1979; Bobko and Roth 2004; Sobol and Ellard 1988; Gastwirth and Miao 2009; Hauenstein et al. 2013; Ismail and Kleiner 2001).

The applicant flow may not be acceptable as a comparative population as it may not be representative of those in the general population who would like to apply for the position. Potential applicants may be excluded by the recruitment methods of a company, producing a biased applicant flow. The reputation of a company may also affect the applicant flow. For example, a company may have a history of discriminatory practices or a poor working environment for those who are members of certain social groups. In these cases, the relevant population may consist of those who would apply for the job if there were no barriers to enter the applicant flow.

If the applicant flow cannot be used, then courts may turn to considering the general population of workers. The assumption in this case is that the composition of the general workforce is representative of the population of workers who want the job in question. This can be problematic in that not all the individuals in the general work force may be interested in all jobs, and some jobs may require special training or certification which individuals in the population may not have.

The Supreme Court addressed this issue in the case of Hazelwood School District v. United States, which concerned the hiring of African American teachers in a Missouri school district in the suburbs of Saint Louis. A district court ruling compared the ratio of African American teachers to white teachers to the corresponding ratio of African American students to white students in the school. This decision was appealed to the Court of Appeals, which rejected this comparison and instead used hiring statistics for teachers in the geographic area, which includes the Saint Louis metropolitan area. This move limited the population to those who were qualified for a job that required a teaching certificate. This decision was appealed to the Supreme Court as the school district argued that the Saint Louis school districts had enacted hiring practices that were designed to specifically increase the number of African American teachers. There were many different and complicated legal questions relevant to the case, and the Supreme Court sent the case back to the district court but established that the relevant comparison population is those who possess the required skills for the position—in this case, a teaching certificate.

General populations may be refined in other ways. One of the most common refinements is based on geographical areas for employment opportunities that are unlikely to attract potential employees outside of a local area. In these cases, the local work force may be used for comparison rather than a more global work force. Localization may also be weighted for surrounding areas by the percentage of applications coming from each local area (Shoben 1986). As populations and the work force can shift with time, the periods considered in litigation can be an important aspect of a case as well.

An interesting issue is that the refining of populations in these ways can have consequences in terms of statistical theory and interpretation. In fact, these methods can be used to manipulate the data analysis, and legal officials may not always be aware of this tactic (Kahneman et al. 1982). Some of these issues will be discussed later.

In cases where a work requirement is challenged, the issues of the relevant population changes slightly. Here the main question is whether a work requirement is discriminatory as opposed to the hiring process of the employer. In these cases, the pool of applicants is not the correct population for comparison purposes because applicants who may have been discriminated against by the work requirement have already been excluded from the population. Hence, the focus must be on the population of potential employees who might wish to apply for the job. This was the case in the Supreme Court case Dothard v. Rawlinson, where a claim that a height requirement for Alabama prison guards disproportionately excluded women. The defendants in the case sought to use the applicant pool, but this idea was rejected because the height requirement was known to the applicants, and therefore those who did not fit the requirement did not apply. To see why this is a problem, suppose that half of the population of possible applications identified as women. If there was no hiring bias, one would expect that roughly half of those hired would be women. Now suppose that 50% of the women in the population of potential applicants meet the height requirement while 90% of the remaining potential employees meet the height requirement. It can be shown that about 36% of the applicant pool will identify as female. If the defendant was allowed to use the applicant pool, they could argue that only 36% of the hired worked force should be female.

Figure \(\PageIndex{1}\) demonstrates how this calculation is accomplished using a small population of 20 individuals. In this population, there are 10 potential applicants who identify as female, and 10 applicants who do not. In the left column of the figure are shapes representing the potential applicant pool, with squares representing the female potential applicants and circles representing the remaining potential applicants. The potential applicants that satisfy the height requirement are indicated in blue, and those who do not are indicated in red. Because half of the population of potential female applicants satisfies the height requirement, five of the ten squares are indicated in blue. Because 90% of the remaining population satisfies the height requirement, nine of the ten circles are indicated in blue. Only the applicants who satisfy the height requirement will apply for the job, and so only the blue shapes proceed to the applicant pool. Therefore, in this simple example, the applicant pool will have five applicants who who identify as female and nine other applicants. Hence, there are 5 individuals in the applicant pool. Computing the percentage of female applicants is then accomplished using the calculation

\[\frac{5}{5+1}\times 100\% = \frac{5}{14}\times 100\% = 36\%. \nonumber\]

Figure \(\PageIndex{1}\): An example showing how a height requirement reduces the percentage of female applicants for employment. In the left column shapes represent the potential applicant pool, with squares representing the female potential applicants and circles representing the remaining potential applicants. The potential applicants that satisfy the height requirement are indicated in blue, and those who do not are indicated in red. (Public domain image created by Alan M. Polansky)

In the case of Dothard v. Rawlinson the Supreme Court used national demographic figures to consider the case. The court ruled in an 8 to 1 decision that the height restriction was discriminatory. The basis of this decision was because the defendants had not proven that the height standard was necessary for effective job performance. Essentially it was found that the defendants were using the height requirement—which was not necessary for job performance—to exclude women from the applicant pool.