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Observational Studies 4 (2018) 17-31 Submitted 12/17; Published 1/18 The Potential Usefulness of Bross’s Principles of Statistical Criticism for the Evaluation of Statistical Evidence in Law and Public Policy Joseph L. Gastwirth Department of Statistics George Washington University Washington, DC 20052, USA 1. Introduction The classic paper by Bross (1960) should be read in conjunction with Cornfield’s inequality, in the appendix of Cornfield, Haenszel et al. (1959) and described in Gastwirth (1988), Greenhouse (1982), Greenhouse (2009), Rosenbaum and Krieger (1990) and Rosenbaum (2002). The inequality states conditions that a suggested omitted variable needs to satisfy in order to “explain” a difference in the proportions of successes (or failures) between two groups. Many extensions of the original result allowing for sampling error or matched pairs and other designs have been developed over the years (Rosenbaum, 2002; Guo at al. 2013) and suggested for use in legal cases (Gastwirth, 1992). Although one may question the thoroughness of the analysis of the data in Table I of the article, the criteria Bross gives for statistical criticism remain relevant today.1 This commentary will focus on the applicability of the framework suggested by Bross for the evaluation of criticisms of statistical evidence in law and public policy as other commentators will discuss the advances in statistical methodology that provide a more comprehensive analysis of epidemiologic and related data sets. Section 2 reviews the role of statistical evidence in discrimination cases. These cases are brought under civil, rather than criminal law, so the trier of fact (jury or judge) decides the case based on the preponderance of the evidence or “more likely than not” standard, rather than the “beyond a reasonable doubt” standard used in criminal cases. Section 3 discusses how courts have considered criticisms of statistical evidence. Because our focus is on the usefulness of Bross’s principles, some important legal aspects, such as whether the cases discussed in Section 3 concerned an appeal of a summary judgment or were a class action will not be emphasized.2 Section 1 Table I examines the death rates of many diseases, however, most toxic agents only affect one or a few diseases, e.g. workers exposed to benzene have an increased risk of leukemia. The sign test gives equal weight to each of the types of mortality, although epidemiologic studies had shown that smoking had a strong association with lung cancer. Statistical methods designed to detect trends in dose-response data, e.g. the Cochran-Armitage (1954, 1955) test or its extension (Mantel, 1963) to stratified data or combining the results of several studies would be more powerful. 2 When a party moves for summary judgment, it is claiming that the opposing party has no case and the entire case should end. Summary judgment is warranted when “the pleadings, depositions, answers to interrogatories and admissions on file, together with the affidavits, if any, show that there is no genuine issue c ⃝2018 Joseph Gastwirth. Gastwirth 4 describes the main studies that led to warning the public about the association between the use of aspirin to treat children with colds or chicken pox and their risk of subsequently developing a rare but serious disease, Reye Syndrome. Because the industry was able to raise questions about the early studies, without being held to the criteria stated by Bross (1960), slightly over three years elapsed from the time the FDA (November, 1982) felt the public should be notified and the start of the warning campaign in the United States in early 1985. 2. The Role of Statistical Evidence in Disparate Impact and Disparate Treatment Discrimination Cases There are two categories of EEO cases, disparate impact and disparate treatment. Disparate impact cases concern the legitimacy of a job requirement, e.g. passing a written or physical test or possessing a certain level of education. When the proportion of applicants from a legally protected group, typically a race-ethnic minority or females, satisfying the requirement is significantly less than the corresponding proportion of majority applicants, an employer has the opportunity to discredit the plaintiffs’ analysis by showing that the data contain serious errors or omit a major relevant variable...


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pp. 17-31
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