We propose a new robust Jarque–Bera (RJB) test utilizing a robust measure of variance. The RJB statistic is asymptotically
χ
2
2-distributed and has equal or higher power than the JB test for several ...common alternatives to normality.
Originally, 2‐stage group testing was developed for efficiently screening individuals for a disease. In response to the HIV/AIDS epidemic, 1‐stage group testing was adopted for estimating prevalences ...of a single or multiple traits from testing groups of size q, so individuals were not tested. This paper extends the methodology of 1‐stage group testing to surveys with sample weighted complex multistage‐cluster designs. Sample weighted‐generalized estimating equations are used to estimate the prevalences of categorical traits while accounting for the error rates inherent in the tests. Two difficulties arise when using group testing in complex samples: (1) How does one weight the results of the test on each group as the sample weights will differ among observations in the same group. Furthermore, if the sample weights are related to positivity of the diagnostic test, then group‐level weighting is needed to reduce bias in the prevalence estimation; (2) How does one form groups that will allow accurate estimation of the standard errors of prevalence estimates under multistage‐cluster sampling allowing for intracluster correlation of the test results. We study 5 different grouping methods to address the weighting and cluster sampling aspects of complex designed samples. Finite sample properties of the estimators of prevalences, variances, and confidence interval coverage for these grouping methods are studied using simulations. National Health and Nutrition Examination Survey data are used to illustrate the methods.
Joseph L. Gastwirth and Qing Shi use three decades of data from a triennial survey of consumer finances to calculate the “number of families needed” to equal the wealth of the Forbes 400 rich list
...Joseph L. Gastwirth and Qing Shi use three decades of data from a triennial survey of consumer finances to calculate the “number of families needed” to equal the wealth of the Forbes 400 rich list.
The Cochran-Armitage trend test is commonly used as a genotype-based test for candidate gene association. Corresponding to each underlying genetic model there is a particular set of scores assigned ...to the genotypes that maximizes its power. When the variance of the test statistic is known, the formulas for approximate power and associated sample size are readily obtained. In practice, however, the variance of the test statistic needs to be estimated. We present formulas for the required sample size to achieve a prespecified power that account for the need to estimate the variance of the test statistic. When the underlying genetic model is unknown one can incur a substantial loss of power when a test suitable for one mode of inheritance is used where another mode is the true one. Thus, tests having good power properties relative to the optimal tests for each model are useful. These tests are called efficiency robust and we study two of them: the maximin efficiency robust test is a linear combination of the standardized optimal tests that has high efficiency and the MAX test, the maximum of the standardized optimal tests. Simulation results of the robustness of these two tests indicate that the more computationally involved MAX test is preferable.
Although the U.S. Supreme Court accepted statistical evidence in cases concerning discrimination against minorities in jury pools and equal employment in 1977, several misinterpretations of the ...results of statistical analyses still occur in legal decisions. Several of these problems will be described and statistical approaches that are more reliable are presented. For example, a number of opinions give an erroneous description of the p-value of a statistical test or fail to consider the power of the test. Others do not distinguish between an analysis of a simple aggregation of data stratified into homogeneous subgroups, and one that controls for subgroup membership. Courts have used measures of 'practical significance' that lack a sound statistical foundation. This has led to a split in the Circuits concerning the appropriateness of 'practical' versus 'statistical' significance for the evaluation of statistical evidence.
A recent article proposed a histogram-based method for estimating the Lorenz curve and Gini index from grouped data that did not use the group means reported by government agencies. When comparing ...their method to one based on group means, the authors assume a uniform density in each grouping interval, which leads to an overestimate of the overall average income. After reviewing the additional information in the group means, it will be shown that as the number of groups increases, the bounds on the Gini index obtained from the group means become narrower. This is not necessarily true for the histogram method. Two simple interpolation methods using the group means are described and the accuracy of the estimated Gini index they yield and the histogram-based one are compared to the published Gini index for the 1967-2013 period. The average absolute errors of the estimated Gini index obtained from the two methods using group means are noticeably less than that of the histogram-based method. Supplementary materials for this article are available online.
Received August 2014. Revised September 2015.
Genetic risks and genetic models are often used in design and analysis of genetic epidemiology studies. A genetic model is defined in terms of two genetic risk measures: genotype relative risk and ...odds ratio. The impacts of choosing a risk measure on the resulting genetic models are studied in the power to detect association and deviation from Hardy–Weinberg equilibrium in cases using genetic relative risk. Extensive simulations demonstrate that the power of a study to detect associations using odds ratio is lower than that using relative risk with the same value when other parameters are fixed. When the Hardy–Weinberg equilibrium holds in the general population, the genetic model can be inferred by the deviation from Hardy–Weinberg equilibrium in only cases. Furthermore, it is more efficient than that based on the deviation from Hardy-Weinberg equilibrium in all cases and controls.
•The relationships between GR and OR at the disease locus are obtained.•The relationships between GR and OR at the marker locus are obtained.•The procedures for choosing the genetic model is proposed.
We present a new R software package lawstat that contains statistical tests and procedures that are utilized in various litigations on securities law, antitrust law, equal employment and ...discrimination as well as in public policy and biostatistics. Along with the well known tests such as the Bartels test, runs test, tests of homogeneity of several sample proportions, the Brunner-Munzel tests, the Lorenz curve, the Cochran-Mantel-Haenszel test and others, the package contains new distribution-free robust tests for symmetry, robust tests for normality that are more sensitive to heavy-tailed departures, measures of relative variability, Levene-type tests against trends in variances etc. All implemented tests and methods are illustrated by simulations and real-life examples from legal cases, economics and biostatistics. Although the package is called lawstat, it presents implementation and discussion of statistical procedures and tests that are also employed in a variety of other applications, e.g., biostatistics, environmental studies, social sciences and others, in other words, all applications utilizing statistical data analysis. Hence, name of the package should not be considered as a restriction to legal statistics. The package will be useful to applied statisticians and "quantitatively alert practitioners" of other subjects as well as an asset in teaching statistical courses.
The increase in income inequality, due to a shift in favor of the upper end in the United States and other countries, has become a public policy concern. This paper shows that the Gini index, G, ...underestimates the rate of increase in inequality because a shift of income towards the top incomes increases both the numerator and denominator of G. A modified index (G_2), which replaces the mean in the denominator by the median, indicates that income inequality in the United States grew at about twice the rate as the Gini index from 1967 to 2012. The analysis accounts for the effect of the changes made in the survey collection process in 1994. In contrast with the United States, while income inequality increased in Sweden, the shift in favor of the upper income region was less pronounced. The index G_2 is readily computed from the mean, median and Gini index, published by many national statistical agencies. Although G_2 may not be appropriate for some analytic purposes, it is an easily calculated summary descriptive measure that is more sensitive to important changes in the income distribution than the Gini index. Most other indices placing greater weight on the upper end of the income distribution must be calculated from micro-data.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
In the 1980s, reports from Congress and the Government Accountability Office (GAO) presented statistical evidence showing that employees in the Foreign Service were overwhelmingly White male, ...especially in the higher positions. To remedy this historical discrimination, the State Department instituted an affirmative action plan during 1990-1992 that allowed females and race-ethnic minorities to apply directly for mid-level positions. A White male employee claimed that he had been disadvantaged by the plan. The appellate court unanimously held that the manifest statistical imbalance supported the Department's instituting the plan. One judge identified two statistical issues in the analysis of the data that neither party brought up. This article provides an empirical guideline for sample size and a one-sided Hotelling's T
2
test to answer these problems. First, an approximate rule is developed for the minimum number of expected minority appointments needed for a meaningful statistical analysis of under-representation. To avoid the multiple comparison issue when several protected groups are involved, a modification of Hotelling's T
2
test is developed for testing the null hypothesis of fair representation against a one-sided alternative of under-representation in at least one minority group. The test yields p-values less than 1 in 10,000 indicating that minorities were substantially under-represented. Excluding secretarial and clerical jobs led to even larger disparities.
Supplemental materials for this article are available online.
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