Reply: Hypotheticals and Hypotheses

Mintz and Dixon offer a plausible hypothetical, but a fairly implausible hypothesis. By a hypothetical we mean a claim that a particular conclusion would follow from a particular premise, with no claim that either the premise or the conclusion is true. A hypothetical is what Nelson Goodman (1965), for instance, calls a "counterfactual conditional" or a statement about a "possible world." Clark Glymour (1986) offers a typical example: ".... if I had been a girl, I would have been named Olga." A hypothetical may be correct as a hypothetical even if it is wrong front and back, that is, even if both the premise and the conclusion are wrong as descriptions of the actual world. Clark is not a girl and was not named Olga, but the hypothetical may nonetheless be true as a hypothetical. Some hypotheticals are important and true as hypotheticals, for instance: "if xl, x2,... is a Cauchy sequence of real numbers, then the sequence converges to a limit." By a hypothesis we mean a claim, perhaps tentative or ultimately erroneous, that something is actually true, and moreover, a claim that is at risk of being refuted on the basis of empirical observations. In this sense a hypothesis is what Sir Karl Popper (1965) calls a "conjecture." Popper discusses carefully and at length what is meant by saying that a conjecture is at risk of refutation, but suffice it to say here that a conjecture must be sufficiently specific about something that can be observed that observations can lead to strong evidence against the conjecture. Hypotheticals and hypotheses may be true or false, plausible or implausible, believed correctly or incorrectly, but they are, nonetheless, very different claims. Consider the sentence: If there were a single quantity called "cognitive ability," if this one quantity were a major determinant of successful performance in clerical work at the Revenue Service, if test scores were reliable and valid measures of this quantity, and if men had vastly more "cognitive ability" than women at the Revenue Service, then this large unobserved disparity in cognitive ability would be a business necessity, justifying promotion of men at twice the rate of women. That sentence is a hypothetical. Consider an alternative sentence: There is a single quantity called "cognitive ability," and it determines successful clerical work at the National Revenue Service, and the test is a reliable and valid measure of this quantity, and moreover, men employed in clerical jobs at the Revenue Service have vastly more "cognitive ability" than similarly employed women, so this large unobserved disparity in cognitive ability between men and women is a "business necessity," and it justifies promoting men at twice the rate of women. The alternative sentence is a hypothesis. The hypothetical is not implausible as a hypothetical, but as with poor, counterfactual Olga, the hypothetical may be false front and back. The hypothesis does not strike us as particularly plausible. Mintz and Dixon even say that they do not regard the hypothesis as plausible. They present calculations that support the hypothetical, but no evidence in support of the hypothesis. So Mintz and Dixon have offered a plausible hypothetical, but neither they nor we regard it as a particularly plausible hypothesis. Consider, now, the legal context into which their hypothetical is offered. The courts have established guidelines for the shifting burdens of production of evidence in discrimination cases. Although the data arose in a disparate impact case, the framework the Supreme Court laid. out in the disparate treatment case, Texas Dep't. of Comm. Affairs v. Burdine, 450 U.S. 248 (1981) describes the burden of production placed on a defendant who needs to respond to a legally meaningful and statistically significant disparity. The opinion states that the defendant needs to "produce evidence that the plaintiff was rejected or someone else was preferred for a legitimate non-discriminatory reason" and "[t]he explanation provided must be legally sufficient to justify a judgment for the defendant." Then the factual inquiry proceeds to a new level of specificity as the plaintiff now has the opportunity of showing that the defendant's reason was not the true reason, and by persuading the Court that a discriminatory reason more likely motivated the employer. In discussing the defendant's burden of production, the Court noted that the defendant's reason should "frame the factual issue with sufficient clarity so that the plaintiff will have a full and fair opportunity to demonstrate pretext. The sufficiency of the defendant's evidence should be evaluated by the extent to which it fulfills these functions." Thus the Court is requiring the defendant to provide substantial, tangible evidence in support of what we have called a hypothesis, not merely to assert a hypothetical. The hypothesis above concerns, not just the claim that men employed in clerical positions at the Revenue Service have vastly more "cognitive ability" than women, but also that this leads to job-related characteristics that are necessary to the business. As the Supreme Court stated in Griggs v. Duke Power Co., 91 S.Ct. 849 (1971), "The Act proscribes not only overt discrimination but also practices that are fair in form but discriminatory in operation. The touchstone is business necessity. If an employment practice which operates to exclude Negroes cannot be shown to be related to job performance, the practice is prohibited." The opinion goes on to state that although the Civil Rights Act of 1964 allows employers to use tests or other measures, "Congress has forbidden giving these devices and mechanisms controlling force unless they are a demonstrably reasonable measure of job performance." Joseph L. Gastwirth is Professor, Department of Statistics, George Washington University, Washington, DC 20052. Abba M. Krieger is Professor and Paul R. Rosenbaum is Professor, Department of Statistics, University of Pennsylvania, Philadelphia, PA 19104-6302.