A murky business Jeong, Yujin; Gastwirth, Joseph L.
Significance (Oxford, England),
02/2015, Letnik:
12, Številka:
1
Journal Article
Odprti dostop
Corruption in Iraq's Oil‐for‐Food Programme was exposed a decade ago. But key information remains unpublished – information that could shed further light on the impact of bribes paid to Saddam ...Hussein's regime. By Yujin Jeong and Joseph L. Gastwirth
Corruption in Iraq's Oil‐for‐Food Programme was exposed a decade ago. But key information remains unpublished
We will show that the regression approach to estimating the standard error of the Gini index can produce incorrect results as it does not account for the correlations introduced in the error terms ...once the data are ordered. To assess the effect of ignoring the correlation in the error terms we examined two distributions and show that the regression method overestimates the standard error of the Gini index. We recommend that the more mathematically complex or computationally intensive methods be used.
Methods for single marker association analysis are presented for binary and quantitative traits. For a binary trait, we focus on the analysis of retrospective case-control data using Pearson's ...chi-squared test, the trend test, and a robust test. For a continuous trait, typical methods are based on a linear regression model or the analysis of variance. We illustrate how these tests can be applied using a public available R package "Rassoc" and some existing R functions. Guidelines for choosing these test statistics are provided.
The substantial increase in economic inequality in favor of the upper income group in the United States and many other developed and developing nations during the past 30 years has become a major ...concern in public policy. Modifications of the standard measures of inequality, the Lorenz curve and Gini index, are proposed that better reflect the decline in the share of income received by the poor and middle portions of the income distribution relative to the upper end. A second pair of curves based on the fractions of either the middle or lower portion of the income curve that has the same share as the top u% and the areas between them and the line of equality are introduced. The proposed curves and related measures indicate that a noticeably greater change in the U.S. income distribution occurred during the 1967-2013 time period than are observed in the Lorenz curve and Gini index. The maximum difference between the proposed curves for the income and wealth data in the United Kingdom's 2010-2012 survey are greater than that of the Lorenz curve.
Background: Cancer screening rates vary substantially by race and ethnicity. We applied the Peters-Belson approach, often used in wage discrimination studies, to analyze disparities in cancer ...screening rates between different groups using the 1998 National Health Interview Survey. Methods: A regression model predicting the probability of getting screened is fit to the majority group and then used to estimate the expected values for minority group members had they been members of the majority group. The average difference between the observed and expected values for a minority group is the part of the disparity that is not explained by the covariates Results: The observed disparities in colorectal cancer screening (5.88%) and digital rectal screening (8.54%) between white and black men were explained fully by the difference in their covariate distributions. Only half of the disparity in the observed screening rates (13.54% for colorectal and 17.47% for digital rectal) between white and Hispanic men was explained by the difference in covariates between the groups. The entire disparity observed in mammography screening rates for black and Hispanic women (2.71% and 6.53%, respectively) compared with white women was explained by the difference in covariate distributions Conclusions: We found that the covariates that explain the disparity in screening rates between the white and the black population do not explain the disparity between the white and the Hispanic population. Knowing how much of a health disparity is explained by measured covariates can be used to develop more effective interventions and policies to eliminate disparity.
Before searching people or property, police need "probable cause." In United States v. Place, the Supreme Court held that dog sniffs of vehicles, stopped for lawful purposes, are not a search. Lower ...courts have held that a positive alert by a trained narcotics dog can establish probable cause for a search of the car. Many courts use the fraction of positive identifications in which drugs were found to assess the reliability of the dog, and thus to decide whether the alert established probable cause. In the medical test literature, this summary statistic is called the predictive value of a positive test (PVP). By itself, it does not measure the accuracy of the sniffs or medical test. There are two components to assessing the accuracy of a dog sniff or test. These are the probability that the dog sniff correctly classifies an item containing contraband as having it and the probability the sniff correctly exonerates an item not containing contraband. The PVP depends on both these probabilities and on the prevalence of contraband in the places the dog has examined. The same PVP can arise when (1) an accurate dog sniffs items with a low prevalence of contraband and (2) a much less accurate dog examines items with a high prevalence of drugs. It is mathematically impossible to estimate the two accuracy rates of a narcotics dog from the field performance data typically submitted by the state to show the narcotics dog is reliable. The problem arises because one needs three equations to estimate the prevalence and the two accuracy rates but the data only provide two. These issues will be illustrated on data from cases. Furthermore, the number of test sniffs in many certifications is too small to provide a statistically reliable measure of the dog's accuracy and the prevalence of drugs in the items sniffed is usually at least 50%. Rather than continuing to rely on an inappropriate measure of the accuracy of dog sniffs, courts should require more information concerning the accuracy of dogs in their training sessions, certifications, and in the field. In conjunction with obtaining better information on the prevalence of drugs in commonly occurring settings—such as vehicles stopped for routine traffic violations or items examined after police have received a "tip"—having access to dog accuracy rates would provide the legal system with sufficient information to estimate both measures of accuracy of a narcotics dog and its PVP, which would assist courts in determining whether the police had probable cause.
In equal employment cases concerning fair hiring or promotion, the number of eligible candidates often exceeds the number of available positions. When a group of plaintiffs show that they were ...discriminated against in the selection process, one cannot determine with certainty which ones would have been chosen. Several decisions from the Seventh Circuit observed that this situation is similar to the loss of chance in tort law where due to negligence the survival probability of a patient has been diminished. In both settings the plaintiffs' loss can be regarded as probabilistic, i.e., in the discrimination context they lost their chance of obtaining the job or promotion. This article shows how survival analysis provide statistically sound estimates of the compensation due to a plaintiff. At each time an employment decision is made, all eligible candidates are considered. Job related factors such as seniority or special skill can be incorporated in the estimates of the probability each candidate would be employed or promoted. These probabilities are used to weight the salary differentials to provide an estimate of the lost salary. The loss in accrued pension benefits is also weighted by probability of being promoted before retirement. The methodology is illustrated on data from the Alexander v. Milwaukee promotion discrimination case. The survival analysis also confirmed the original finding of liability as the chances of promotion of white males were statistically significantly lower. Because seniority was an important factor our estimates differ from those suggested in the opinion which followed the Biondo v. City of Chicago decision. That opinion assumed a plaintiff who ultimately received a promotion would have been promoted during the period of discrimination. This assumption is questionable when seniority has a role since an individual's seniority increases over time. PUBLICATION ABSTRACT
The article reviews the use of statistical tests to establish a prima facie case that an exam has a disparate impact on minorities. Two common scenarios are discussed. The first is that promotions ...are made in accordance with the 'rank-order' of the exam scores or a composite of the exam scores and some other factors. Courts have used several statistical tests in this situation, which may lead to conflicting conclusions from similar data. It will be shown that when the spreads of the exam scores in both groups are close to each other, the modified Wilcoxon test has desirable statistical properties. When the spreads of the exam scores of the two groups are noticeably different, a two-test procedure is proposed and shown to have higher power, especially when the spread of the minority scores is less than that of the majority. The second situation occurs when once an applicant passes the exam, s/he is eligible for further consideration and the actual exam score no longer matters. Courts may need to consider both the practical and statistical significance of the difference in pass rates. Small, unimportant differences may reach statistically significance when the numbers of applicants are large. In contrast, large differences in pass rates may not be detected as statistically significant in small samples. Two tables are provided to assist courts in reaching more consistent decisions when statistical and practical significance may not agree. PUBLICATION ABSTRACT
Case-control studies are commonly used to study whether a candidate allele and a disease are associated. However, spurious association can arise due to population substructure or cryptic relatedness, ...which cause the variance of the trend test to increase. Devlin and Roeder derived the appropriate variance inflation factor (VIF) for the trend test and proposed a novel genomic control (GC) approach to estimate VIF and adjust the test statistic. Their results were derived assuming an additive genetic model and the corresponding VIF is independent of the candidate allele frequency. We determine the appropriate VIFs for recessive and dominant models. Unlike the additive test, the VIFs for the optimal tests for these two models depend on the candidate allele frequency. Simulation results show that, when the null loci used to estimate the VIF have allele frequencies similar to that of the candidate gene, the GC tests derived for recessive and dominant models remain optimal. When the underlying genetic model is unknown or the null loci and candidate gene have quite different allele frequencies, the GC tests derived for the recessive or dominant models cannot be used while the GC test derived for the additive model can be.
The North Carolina Racial Justice Act allows defendants to submit statistical studies of prosecutorial actions pertaining to their seeking the death penalty or in making peremptory challenges. These ...studies may consider data from four geographical regions: the state, county, judicial division or prosecutorial district. A study of the effect of race on peremptory challenges in death penalty cases demonstrating statistically significant disparities disadvantaging Black defendants has been submitted in several cases. This comment shows that a more appropriate statistical analysis yields much stronger statistical evidence that race entered into the peremptory challenge process in Randolph County than the affidavit submitted by the authors of the study. A subsequent sensitivity analysis indicates that in order for a characteristic to explain the highly statistically significant disparity, it would need to increase the odds of an individual being challenged by a factor of three and more than twice as many Black venire members would need to possess that characteristic as non-Blacks. Since the data examined excluded potential jurors who had been removed for cause, it may be difficult for the state to find a legitimate reason justifying the racial disparity. PUBLICATION ABSTRACT
PDF
