Adjusting the Odds


Just as you may have used statistics to resolve issues for others, you too may benefit from their judicious use. There may be times when hiring, promotion, tenure, or other decisions don’t go your way; you may feel the adverse result is not based on merit, but rather may be the result of discrimination. What recourse might you have?

There are laws that prohibit discrimination on the basis of race, gender, national origin, religion, age, and disability, but benefiting from legal protections can be difficult. Those of us who have been around awhile can remember when admission to graduate programs was specifically denied to women or jobs were listed in separate columns by gender, but overt gender discrimination is rare these days—and hard to prove even when it occurs. Lack of success is more likely to result from a series of microaggressions—sometimes characterized as “a thousand blows” or as implicit bias, although the bias is often not unconscious at all.

Statistics have proven useful in certain circumstances, but the task of proof is not an easy one. Fundamental may be showing that you are not the only victim; here, statistics may increase your chances of success.

Under various statutory provisions, there are two kinds of discrimination. Disparate treatment consists of treating someone differently on the basis of some protected characteristic. The “white only” signs that used to be affixed to restrooms, drinking fountains, housing, and elsewhere made this kind of discrimination pretty clear. “No Irish need apply” used to be endemic in certain cities; real estate covenants in the past prohibited Jews; and, as noted above, education and employment gender restrictions were common. In a more-personal manifestation of discrimination, one might be denied a certain position because of a stereotypical view that it is “not a job for a woman” (maybe especially one with children).

More subtly, but just as harmful among the obstacles that can occur, are that the ideas expressed by a woman are ignored until promoted and claimed by a man; that “boy” is applied to an African American man; that there is an outcry of “Islamic terrorists” should a tragedy occur; that preference is given to white male diners, airline passengers, or shoppers in electronics.

But in addition to these explicit discriminatory encounters, there is disparate impact discrimination; that is, although a practice or policy may be facially neutral and thus not overtly discriminatory, the result is.

For example, in a seminal case, the requirement of an electric company line service workers be high school graduates was found to have a discriminatory racial impact because the percentage of African Americans in North Carolina with high school degrees was considerably less than the percentage of whites, and it was also the case that many white linemen were completely effective without the benefit of such education; thus, it was not a legitimate job requirement, but rather illegal because of its discriminatory impact.

Similarly, height requirements that are not necessary for the performance of a job have been found to have a disparate gender and racial impact. Sherlock Holmes may have been the only resource in a case involving a preference for red-haired individuals, but today, this might be found to have an adverse national origin impact, and the scheme could not have been implemented legally even if robbery were not the goal.

Clearly, statistics play a big role in determining impact—we need to know that a requirement disproportionately disqualifies those in a protected category, and then we may need to know how crucial that requirement really is to performance of the task at hand.

Justification for a qualification that has a discriminatory impact in the employment context is generally characterized as “business necessity.” Even in the case of disparate treatment, it may be useful to show that other women—here we cite gender discrimination, but the same is true in race or national origin cases—have suffered discrimination.

Litigation is expensive, so banding a group together in what is termed a “class action” case is a useful technique. Unfortunately, because of court decisions, this has become increasingly difficult in recent years. However, even in the case of a single complainant, statistical evidence of similar discriminatory conduct may be helpful; dozens, if not hundreds, of regression studies of salaries in higher education have shown that women, on the average, are paid less than men even when measurable characteristics are the same.

Of course, the problem is that there are always other variables that might be included and that might explain the gender disparity, so the evidence showing discrimination is not always clear, either to employers themselves in internal studies or to the courts. Nonetheless, properly done, such investigations can be a powerful tool in remedying inequities or sometimes in showing that there are none.

Extensive challenges for the use of statistics to prove that there is discrimination also can be seen—or more properly, to show that, absent discrimination, intentional or not, such results would not occur. Who is eligible for the job, for admission, to serve on a jury, and how do those numbers compare with those who have been successful?

While a finding of illegal disparate treatment requires showing an intent to discriminate, no intent to discriminate must be shown when disparate impact discrimination is impermissible under statutory provisions. In general, whether disparate impact is illegal depends on statutory language or intent as interpreted by the courts. However, even when intent to discriminate must be shown, statistics can be helpful.

For example, beyond statutory protection, equal treatment is, in theory, promised by the 14th Amendment to the United States Constitution:

No state shall make or enforce any law which shall abridge the privilege or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

But it is important to remember that the Constitution protects one only against acts of the government in its various forms and not against private employers or other entities, whose acts may, however, be subject to specific legislation prohibitions.

In a recent case, North Carolina voting law restrictions were found to be unconstitutional because it was shown that the legislature made use of statistics to show, “with almost surgical precision” as the U.S. Supreme Court said, that changes in the law targeted procedures in a way that would disproportionately affect African American voters. Provisions intended to prevent voter fraud might serve the “rational purpose” required by the least-strict form of constitutional review, but the numbers showed that the legislature’s actual purpose was to suppress the votes of targeted portions of the electorate.

Certain forms of discrimination have withstood constitutional scrutiny—only in 1954 did the Supreme Court decide that the doctrine of “separate but equal” did not justify racially segregated public schools. That separate might be equal with respect to gender has been permitted under a less-stringent form of judicial review.

Race distinctions are subject to “strict” scrutiny: They must serve an important government purpose and there must be no less-discriminatory way to accomplish that purpose. Gender restrictions are examined at the less-restrictive “intermediate” level: They must further an important government interest by means that are substantially related to that interest. The Supreme Court upheld sex segregation in schools after Brown v. Board of Education outlawed racial segregation in 1954. Along the way, however, men gained entry to Mississippi University for Women, 18-year-old men were allowed to drink 3.2 beer, and the spouses of female military officers got the same benefits as spouses of male officers, until finally, in 1996, the court required the Virginia Military Institute to admit women.

Recently, the Supreme Court has found gender discrimination in marriage law unconstitutional; draft registration is still required only for males, but policy has mandated the opening of combat service to women. Remaining gender inequities would (in theory) be eliminated were the Equal Rights Amendment, passed by Congress in 1972 but not ratified by the states, to be adopted: Equality of rights under the law shall not be denied or abridged by the United States or by any state on account of sex.

What the law says and what happens is, we know, not the same thing. Nevertheless it is useful to know what legal recourse is available in cases of possible discrimination, particularly in education and employment. We begin by looking at international law and U.S. constitutional law.

The UN Convention to Eliminate Discrimination Against Women (CEDAW) provides for equality in a broad range of settings, such as employment, education, and public services. The United States has not ratified this convention (the only other UN members who have not are Iran, Palau, Somalia, Sudan, South Sudan, and Tonga)—not that all countries that have ratified abide by the convention’s provisions. In any case, U.S. courts are not generally disposed to be moved by international law.

The U.S. Constitution and the Bill of Rights (the first 10 amendments) provided a multitude of rights to men who were not slaves. Then the post-Civil War 14th Amendment purported to give equal rights to everyone (as long as he was male). Subsequently, the 14th Amendment has been used to secure certain rights for women.

There are, of course, legal protections for women beyond employment and education, in particular (at least so far and in an attenuated manner) the right to choose how to control one’s body (Roe v. Wade, 1973). Legislation guaranteeing non-discrimination in housing, transportation, and public accommodation includes sex as a protected category, notwithstanding the current bathroom controversies.

There is also protective legislation that covers women and men, such as the Age Discrimination in Employment Act and the Americans with Disability Act (ADA). For example, the ADA requires that accommodations be made for disabilities, while the Pregnancy Discrimination Act mandates the same for pregnancy. The Occupational Health and Safety Act (1970) requires a safe working environment for everyone (Where’s the nearest restroom? How many hours do you have to work without a break?), and the Fair Labor Standards Act mandates a minimum wage of $7.25, but many cities and states have a much higher threshold that may be relevant for student employees, among others.

This brings to mind the abuse of the unpaid intern concept, although fortunately, that is less likely to be found when the work involves statistics or data science.

The Affordable Care Act eliminated most problematic healthcare issues, but it may not be around forever (or even next year), reintroducing access and cost issues, particularly for women—such as forbidding co-payments for contraception. Federal law requires only unpaid maternity and family care leave, but again, state or city regulations might be better. Moreover, many employers provide far more general benefits, but often subtly or otherwise discourage their use.

This is a difficult area; a few studies have shown that, in academe, using a benefit may have long-term adverse effects. For example, delaying a tenure decision may lead to a greater risk of denial.

State and city statutes sometimes provide more protection than is available at the federal level—for example, covering marital status, student status, a broader range of age discrimination, or stronger prohibition of sex discrimination. In the case of education, while the Supreme Court did not apply to sex, when the Brown v. Board of Education finding that separate cannot be equal was applied in a case involving Central High School in Philadelphia, the Pennsylvania state constitution equal protection provision was found to guarantee equal access to women.

Although Title IX generally prohibits sex discrimination in education, its early successes were most notably in sports, with the past decades of victories by U.S. women in the Olympics attributed to the opportunities it made available. But the scope of Title IX is much broader. Now we hear not only of its prohibition against sexual harassment and assault, but also of how to deal fairly with everyone involved in reported cases. Although whether appropriate instruction in calculus was available was at issue in the Philadelphia schools case, there has been little litigation about adverse treatment of women (or of men) students in certain disciplines. It is important to note that prohibited discrimination includes not only disparate treatment, as discussed above, but also the creation of a “hostile environment.”

What, then, is the underlying basis for the use of statistics in employment or education litigation? The proportion of beneficiaries who are women can be compared with the proportion of those eligible for the benefit and, finding a disparate impact, one can ask whether the discrepancy could have occurred by chance were selection free of discrimination.

Of course, there are limitations. One is guaranteed equal pay only for equal work, not for comparable work, and rejected applicants must have the same qualifications as those who succeed. But what qualifications are the same? Is a PhD in statistics the same as a PhD in biostatistics; how many years experience do rivals have; do we care about quality of publications or only about quantity? Nearly every university has struggled to answer these questions, as have many other employers.

Many times, it is a question of who makes the decisions. For example, in Wal-Mart Stores, Inc. v. Dukes (2011), the Supreme Court held that decision-making was too distributed to allow comparison of employees nationwide in a wage suit. To put this in a context relevant to statisticians, can we compare across departments or across divisions or colleges? A rule of thumb might be that complainants seek a larger group for comparison purposes, while employers seek to shrink the comparison cadre, since we all know the influence of sample size. Courts have a regrettable tendency to follow much of the research community in placing an almost mystical importance on p-values, but that is a topic for another time and place.

Many have observed that the longer women are employed, the larger the salary discrepancies on average. A Supreme Court decision held that remedy must be sought at the time of the initial discrimination even if it had gone on, and indeed worsened, over the years. The 2009 Lilly Ledbetter Act fixed that loophole in protection.

Title VII of the Civil Rights Act of 1964 forbids discrimination in employment on the basis of sex and other protected attributes. Of course, it is not simple. At one stage, the Supreme Court said pregnancy benefits could be excluded from health insurance coverage because pregnant men were also excluded. Congress passed the Pregnancy Act (1978) to remedy that problem.

It was claimed that men could receive more in periodic pension payments because that was discrimination on the basis of longevity, rather than on the basis of sex.

Establishing the principle of equality in this case took more-complicated statistics than needed to establish the principle in the case of pregnancy benefits, and relief came in the form of a Supreme Court decision (Arizona Governing Committee v. Norris, 1983), rather than through Congress. Further pension equity came through the Retirement Equity Act of 1984, which assured protection of surviving spouses in plans of private employers.

One type of protection that many mistakenly believe they have is First Amendment freedom of speech. Private employers, including private colleges and universities, are not bound by constitutional provisions, although tradition or faculty handbooks may provide somewhat analogous academic freedom protection. Moreover, the First Amendment rights of government employees are severely restricted as far as job protection is concerned.

Let’s be very clear—the purpose here is to make people aware of their rights. It is not to encourage rushing to the courthouse when you believe you have been treated unfairly. In many employment or education cases, there are internal mechanisms—although improving them is generally a good cause in which to enlist (does the institution have an effective ombudsperson policy?). One may report employment, housing, public accommodation, etc., discrimination to state and federal agencies, admittedly with varying degrees of success. Litigation is expensive and difficult, and can be traumatic even for victors. Moreover, the purpose of Title VII, for example, is to “make whole”; that is, you eventually get only what you were entitled to in the first place.

Good advice is to find out your conditions of employment or educational program earlier, rather than later. Solidarity is also useful in most situations, so think about helping your colleagues.

About the Author

Mary Gray, who writes “The Odds of Justice,” is a professor of mathematics and statistics at American University in Washington, DC. Her PhD is from the University of Kansas, and her JD is from the Washington College of Law at American University. A recipient of the Elizabeth Scott Award from the Committee of Presidents of Statistical Societies, she is currently chair of the American Statistical Association Scientific and Public Affairs Advisory Committee. Her research interests include statistics and the law, economic equity, survey sampling, human rights, education, and the history of mathematics.

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  1. Thank you for your comment. We are aware of the error and have reprinted this in the latest Amstat News, and have opened this up to all who read CHANCE magazine.

  2. It might be a nice gesture to include all of this article in the online edition. There appears to be a typographical issue on p.63/p.64 of the print edition. Page 63 ends a sentence, but p.64 starts mid-sentence.

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