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Interpreting group differences observed in aggregated data is a practice that must be done with enormous care. Often the truth underlying such data is quite different than a naive first look would indicate. The confusions that can arise are so perplexing that some of the more frequently occurring ones have been dubbed paradoxes. This article describes two of these paradoxes—Simpson's paradox and Lord's paradox—and illustrates them in a single dataset. The dataset contains the score distributions, separated by race, on the biological sciences component of the Medical College Admission Test (MCAT) and Step 1 of the United States Medical Licensing Examination™ (USMLE). Our goal in examining these data was to move toward a greater understanding of race differences in admissions policies in medical schools. As we demonstrate, the path toward this goal is hindered by differences in the score distributions which gives rise to these two paradoxes. The ease with which we were able to illustrate both of these paradoxes within a single dataset is indicative of how widespread they are likely to be in practice. [ABSTRACT FROM AUTHOR]

When subjects are measured twice, once at each of two symmetrical locations or times, stability of responses in the absence of treatment within subjects, together with comparability of untreated responses between subjects, is often viewed as supporting a conclusion that differences between treated and control responses reflect effects actually caused by the treatment. The degree to which this intuitive argument is formally correct is explored is several related models: a multivariate Normal model, a nonparametric model defined by symmetries, an analogues randomized experiment, and sensitivity analysis model for observational studies in which treatments are not randomly assigned to subjects, nor to locations within subjects. Card and Kreuger's study of the employment effects of the minimum wage is used to illustrate the methods. [ABSTRACT FROM AUTHOR]

Theory and Methods Editor's Note The wisdom of adjusting U.S. decennial census counts and the theory and methods that might be used for that purpose have been matters of hot dispute in certain recent court cases involving expert testimony from numerous leading statisticians and demographers. This article by Ericksen and Kadane and the ensuing comments address the theoretical and practical issues from both sides of the controversy. In order to provide a context for the reader, I am including the following brief history, as it has been explained to me. Between the 1970 and the 1980 decennial censuses, a demand for greater accuracy of census counts arose because of the increased uses of census numbers in fund-allocation formulas for states and other political jurisdictions. The undercount became a particular target of concern, because estimates provided by the Bureau of the Census show that it is more concentrated among blacks than whites, among men than women, and among the young rather than the old. A lawsuit was filed on Census Day, 1980, by the city of Detroit asking for the 1980 census to be adjusted for the undercount. This action was soon followed by other lawsuits with a total of 52 filed, 36 of which asked for adjustment. Two of the adjustment cases have gone to trial--the city of Detroit and the state and city of New York. The other adjustment cases have been resolved or combined into a multidistrict litigation that is still in the pretrial phase. In the Detroit case, the district court ruled in favor of Detroit. When the government appealed, the case was not settled on the merits of adjustment, but was decided on a legal point--that Detroit did not have a standing to bring the case to court. During this case, several statisticians testified for each side. They were Philip Hauser,... [ABSTRACT FROM AUTHOR]

Proof of fact in legal proceedings increasingly involves the use of statistical methods. David Kaye's succinct and informative description of what constitutes illegal discrimination in various contexts provides a legal backdrop for the courtroom stage onto which statistical assessments have been introduced as evidence in discrimination litigation. He also summarizes on how the Supreme Court, both the ultimate legal reviewer and performer, has reacted to statistical evidence in several discrimination cases beginning with Swain v. Alabama, in which the Court ruled in a manner counter to what a good statistical analysis would have suggested. Kaye concludes that the Court "has yet to display an appreciation of the mechanics and assumptions of classical hypothesis testing." In discussing the role of formal statistical inference in discrimination cases Kaye considers (a) classical tests of hypotheses, (b) the presentation of p value, (c) the display of prediction intervals, (d) the presentation of a likelihood function, and (e) a Bayesian treatment.

The future of statistics as a discipline is discussed as are ways to enhance that future. The presentation includes sections on statistics as a discipline, recruitment into the discipline, training in statistics, the unification of statistics, and concluding remarks. The nature of statistics is reviewed with reference to the views of various practitioners of statistics. It is noted that public attitudes to-ward science and statistics are not conducive to the recruitment of students to the discipline and that anticipated shortages of personnel must be met by vigorous efforts to attract the best young people to statistics. Suggestions are made for improved training in statistics and for broader programs in continuing education. It is noted that research in statistics should deal both with topics motivated- by problems of the real world and with the foundations of statistical inference. Specific recommendations are made that should strengthen statistics in the future and lead to its continued unification. The American Statistical Association, enlisting the cooperation of other statistical societies, is seen as the major means of ensuring the future of statistics as a discipline. The ASA must provide the leadership required and represent the discipline to society. [ABSTRACT FROM AUTHOR]

A missing information technique is applied to blood lead data that is both grouped and assumed to be lognormally distributed. These maximum likelihood techniques are extended from the simple lognormal case to obtain solutions for a general linear model case. Various models are fitted to the data, and likelihood ratio statistics are computed to test for significance of various parameterizations. The techniques are applied to a data set of over 130,000 blood lead values collected by the city of New York. The data, collected from 1970 to 1976, are part of a large-scale screening program and have implications for the current ambient air lead standard. [ABSTRACT FROM AUTHOR]