Problems in assessing employment discrimination
指出在反歧视诉讼中，统计推断常假设不可量化的差异源于歧视，这给被告带来沉重负担。作者通过回归分析和外部可用性基准的讨论，揭示了统计检验中隐含的假设问题。
It is now standard practice in the enforcement of antidiscrimination legislation to use statistical analysis, especially in cases where the discriminatory practice is not observed directly, but must be inferred. In the classic example, the demographics of a firm's hiring might be compared to that of the county-wide work force. Plaintiffs in these actions would satisfy part of the requirement for a prima facie case by showing that the firm hired fewer protected group members than would be expected using the benchmark availability for that group. Similar calculations are made in promotion or termination investigations, but the benchmark would be the promotion or termination rates of the firm's own employees who are not charging discrimination. The logic of pay comparisons is the same: if the earnings of protected group members are statistically different from earnings of the benchmark group (usually white males), the defendant is presumed to have failed the statistical test. In each of these situations a defendant confronted with an adverse statistical finding will seek to explain differences in hiring, promotion, or pay by showing that they can be explained by productivity or availability factors.' The problem we draw attention to in this paper arises when dealing statistically with what remains unexplained or unquantifiable. The traditional analysis presumes that unquantifiable differences between protected and nonprotected groups are due to discrimination. Clearly, this presumption may place a difficult, and occasionally impossible, burden on defendants. In Section I we explore the use of regression as an analytical tool and critique the way its results are typically interpreted. In Section II we discuss the use of external availability calculations as benchmarks for the analysis of claims of discriminatory hiring. Using establishment-specific data filed with the federal government, we show that the variation in the representation of demographic groups across establishments greatly exceeds what would occur if all drew employees from the same pool. Judging all employers against a fixed pool implies an extreme assumption about a factor that is unquantifiable from aggregate data, specifically, that there is no underlying variation in availability. The main point of each of these sections is that, in performing statistical tests and giving opinions based on them, one necessarily makes assumptions in the form of maintained hypotheses. We believe that the movement by economists from data summary and presentation in professional journals to statistical inference for the courts has been simplistic. Before moving on to the body of our paper, we would like to mention two additional topics. First, as we have explained elsewhere,2 focusing statistical analysis on a subset of an employer's personnel actions may lead to incorrect inference if the prac* The authors are colleagues at Welch Associates. Robert S. Follett and Michael P. Ward are in Santa Monica, California (1640 Fifth Street, 90401) and Finis Welch is in Bryan, Texas (3833 S. Texas Avenue, #285, 77802) where he divides his time with Texas A&M University and Unicon Research. 'We use the term quantifiable instead of the traditional statistical term observable. In most employment litigation, decisions involving hiring, promotion and pay are rarely, if ever, random decisions. From the viewpoint of an outside observer, however, only a small fraction of observed variation is with employment records. 2Each practice by a large nondiscriminator has a probability of 0.95 that it will appear nondiscriminatory. If the practices are independent, these probabilities may be multiplied. For 14 practices, 0.95 raised to the 14th power is 0.4877, or less than half. (See Follett and Welch, 1983).