In practice, the ultimate outcome of many important discrimination cases, for example, the Wal-Mart, Nike and Goldman-Sachs equal pay cases, is determined at the stage when the plaintiffs request ...that the case be certified as a class action. The primary statistical issue at this time is whether the employment practice in question leads to a common pattern of outcomes disadvantaging most plaintiffs. However, there are no formal procedures or government guidelines for checking whether an employment practice results in a common pattern of disparity. This article proposes using the slightly modified likelihood ratio test and the one-sided Cochran-Mantel-Haenszel (CMH) test to examine data relevant to deciding whether this commonality requirement is satisfied. Data considered at the class certification stage from several actual cases are analyzed by the proposed procedures. The results often show that the employment practice at issue created a common pattern of disparity, however, based on the evidence presented to the courts, the class action requests were denied.
In many applications, the underlying scientific question concerns whether the variances of k samples are equal. There are a substantial number of tests for this problem. Many of them rely on the ...assumption of normality and are not robust to its violation. In 1960 Professor Howard Levene proposed a new approach to this problem by applying the F-test to the absolute deviations of the observations from their group means. Levene's approach is powerful and robust to nonnormality and became a very popular tool for checking the homogeneity of variances. This paper reviews the original method proposed by Levene and subsequent robust modifications. A modification of Levene-type tests to increase their power to detect monotonic trends in variances is discussed. This procedure is useful when one is concerned with an alternative of increasing or decreasing variability, for example, increasing volatility of stocks prices or "open or closed gramophones" in regression residual analysis. A major section of the paper is devoted to discussion of various scientific problems where Levene-type tests have been used, for example, economic anthropology, accuracy of medical measurements, volatility of the price of oil, studies of the consistency of jury awards in legal cases and the effect of hurricanes on ecological systems.
The Gini index is the most commonly used measure of income inequality. Like any single summary measure of a set of data, it cannot capture all aspects that are of interest to researchers. One of its ...widely reported flaws is that it is supposed to be overly sensitive to changes in the middle of the distribution. By studying the effect of small transfers between households or an additional increment in income going to one member of the population on the value of the index, this claim is re-examined. It turns out that the difference in the rank order of donor and recipient is usually the most important factor determining the change in the Gini index due to the transfer, which implies that transfers from an upper income household to a low income household receive more weight that transfers involving the middle. Transfers between two middle-income households do affect a higher fraction of the population than other transfers but those transfers do not receive an excessive weight relative to other transfers because the difference in the ranks of donor and recipient is smaller than the corresponding difference in other transfers. Thus, progressive transfers between two households in the middle of the distribution changes the Gini index less than a transfer of the same amount from an upper income household to a lower income household. Similarly, the effect on the Gini index when a household in either tail of the distribution receives an additional increment is larger than when a middle-income household receives it. Contrary to much of the literature, these results indicate that the Gini index is not overly sensitive to changes in the middle of the distribution. Indeed, it is more sensitive to changes in the lower and upper parts of the distribution than in the middle.
Abstract
On 5 November 2020, the Office of Federal Contract Compliance in the Department of Labor issued new rules codifying the procedures it will use to resolve equal employment issues. First, this ...article summarizes the new rules focusing on how the agency will use and evaluate statistical evidence in its monitoring of government contractors’ compliance with equal employment laws. After noting the diminished role of statistical evidence in the new rules, the likely effect of them on the use of statistical data and analyses in equal employment proceedings are explored. The logical and statistical reasoning underlying several aspects of the new rules is also questioned. Because the new rules refer to a report of the Chamber of Commerce that, in part, criticized the agency from bringing a case against a firm, data from the case are re-analyzed. The statistical analysis provides support for the position of OFCCP.
Civil cases outnumber criminal cases in federal courts, and statistical evidence has become more important in a wide variety of them. In contrast to science, which is concerned with general ...phenomena, legal cases concern one plaintiff or a class of plaintiffs and replication of the events that led to the case is not possible. This review describes the legal process, the way statistics are used in several types of cases, and the criteria courts use in evaluating the reliability of statistical testimony. Several examples of courts' misinterpreting statistical analyses are presented. Commonly occurring issues in the statistical analysis of stratified data, the use of regression analysis, and the use of epidemiologic estimates of relative risk are described. Hopefully, this review will encourage statisticians to engage with the legal system and develop better ways of communicating the results of studies so they receive the evidentiary weight they deserve.
In December 2020, Texas filed a motion to the U.S. Supreme Court claiming that the four battleground states: Pennsylvania, Georgia, Michigan, and Wisconsin did not conduct their 2020 presidential ...elections in compliance with the Constitution. Texas supported its motion with a statistical analysis purportedly demonstrating that it was highly improbable that Biden had more votes than Trump in the four battleground states. This article points out that Texas's claim is logically flawed and the analysis submitted violated several fundamental principles of statistics.
Abstract
The distinction between statistical and practical significance often arises in the analysis of large data sets, where seemingly small disparities can reach statistical significance at the ...0.05 level. In 2014, the opinion in Jones v. Boston created a split in the circuits when it relied solely on statistical significance. The opinion noted that there is no generally accepted definition of practical significance and that the phrase may simply mean that the person using the term views the disparity as substantial enough that a plaintiff should be able to sue. In July 2019, the Office of Federal Compliance Programs (OFCCP) proposed updated procedures for the way it considers both practical and statistical significance when reviewing the employment practices of government contractors.1 On 10 November 2020, the Agency issued its final rules, which downplayed the role of statistical significance.2 The main measures of practical significance mentioned in the notices OFCCP issued in the Federal Register or its Frequently Asked Questions guide3 as well as some other measures of practical significance that have been proposed are studied in this article. The results of the paper support the First Circuit and OFCCP in their views that there is no single measure of practical significance that can be recommended for use as the sole criterion for deciding whether the disparity has practical importance. Nevertheless, the paper includes an empirical guideline combining the odds ratio and difference between success rates to judge practical significance as well as recommendations for balancing Type I and Type II errors and their consequences in the context of the case in determining the level required for statistical significance.
Piketty (Capital in the Twenty First Century; Cambridge MA: Belknap Press) and Dorling (Inequality and the 1%; London: Verso) observed that wealth inequality was increasing at a faster rate than ...income inequality. Wolff (2017) reached the opposite conclusion based on the fact that the Gini index of net worth increased by 9.8% from 1983 to 2016 while the Gini index of income increased by 24.5% over the same period. Because the Gini index does not fully capture changes in a distribution when almost all gains in income or wealth accrue to the upper end, Gastwirth (Statistical Journal of the IAOS; 30:311–320) used a median-based version (G2), which showed that income inequality in the U.S. and Sweden increased at a faster rate than the usual Gini index. Here, analyzing wealth data using G2 shows that wealth inequality increased faster than the Gini index in the U.S. from 1989 to 2019. Similar results are found for Sweden, India and China from 2000 to 2020. A study of the effect of the 2008 financial crisis using the time trend of G2 provides strong evidence that Sweden’s response it decreased wealth inequality, but the reverse was true in the U.S. Canada was the only nation of the six studied where wealth inequality declined over the 2000–2020 period.
Almost all governmental and international agencies use the Gini index to summarize income inequality in a nation or the world. The index has been criticized because it can have the same value for two ...different distributions. It will be seen that other commonly used summary measures of inequality are subject to the same criticism. The Gini index has the advantage that it is able to distinguish between two distributions that have identical integer valued generalized entropy measures. Because no single measure can fully summarize a distribution, researchers should consider combining the Gini index with another measure appropriate for the topic being studied.
Abstract
A proposed rule announced by the Office of Federal Contract Compliance describing the way statistical tests will be used in compliance reviews led to the Chamber of Commerce filing a formal ...Comment. The comment raises several statistical issues, including the proper analysis of stratified data and the effect of large samples on tests of significance. The Chamber correctly pointed out that simple pooling of the data into one large sample can lead to misleading conclusions, so an appropriate analysis, combining the results of statistical analyses of the individual strata into an overall estimate and statistical test is described. Both the proposal and Comment state that practical significance should be considered but do not provide a clear definition of the term, although various definitions are referred to. Two alternative approaches to evaluating the practical significance are described. One assesses the financial impact of the disparity on a typical wage earner, while the second considers the number of employees affected by the disparity and estimates the effect of the disparity on their earnings during their expected time of employment.
PDF
