The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

Visualization for Large‐scale Gaussian Updates

In geostatistics and also in other applications in science and engineering, it is now common to perform updates on Gaussian process models with many thousands or even millions of components. These large‐scale inferences involve modelling, representational and computational challenges. We describe a visualization tool for large‐scale Gaussian updates, the ‘medal plot’. The medal plot shows the updated uncertainty at each observation location and also summarizes the sharing of information across observations, as a proxy for the sharing of information across the state vector (or latent process). As such, it reflects characteristics of both the observations and the statistical model. We illustrate with an application to assess mass trends in the Antarctic Ice Sheet, for which there are strong constraints from the observations and the physics.     

Response Order Effects in Dichotomous Categorical Questions Presented Orally: The Impact of Question and Respondent Attributes

Using data from 548 experiments in telephone surveys conductedby the Gallup Organization, we explored how attributes of questionsand respondents moderate response order effects in dichotomouscategorical questions. These effects were predominantly recencyeffects and occurred most in questions that were more difficultto comprehend (especially among respondents with the least education),with response choices that were more difficult to comprehend(because they were complete sentences instead of words or phrasesand because they were not mutually exclusive), and that wereasked after many prior questions. Recency effects were alsomore common in questions that explicitly or implicitly encouragedrespondents to wait until they had heard all the answer choicesbefore formulating a judgment than in questions that inducedrespondents to begin formulating a judgment before all the answerchoices had been read (especially among the least educated respondents).A study of interviewer behavior revealed patterns of pausingbetween and within sentences that help to explain why some typesof questions are especially prone to recency effects and othersare not.     

Gambling Behavior of Student-Athletes and a Student Cohort: What are the Odds?

This study investigated the prevalence of gambling, gambling related NCAA violations, and disordered gambling in student-athletes (n = 736) with a comparison cohort of students (n = 1,071) at four universities. Student-athletes reported similar rates of gambling frequency, use of a bookmaker, and disordered gambling as students. After accounting for demographic differences, student-athletes were less likely to engage in sports wagering than students. Several risk factors for disordered gambling were identified, including being male and reporting at least one parent with a history of gambling problems. These findings suggest that problems associated with gambling are a university-wide issue with student-athletes meriting additional attention because of implications for the integrity of intercollegiate sports. Improved prevention and intervention efforts for collegiate gambling are recommended.     

Fractured relationships and the potential for abuse of older men

Elderly men are an understudied population in the area of abuse and neglect. The typical elder abuse or neglect victim is described as a frail woman. The National Elder Abuse Incidence Study shows men to be victims as well and at higher risk than women for abandonment, the most extreme form of neglect. A qualitative study of older widowed men did not specifically explore issues of abuse and neglect, but found several of the men experiencing alienation from one or more of their adult children. This paper explores the dynamics of these "fractured relationships" and finds several patterns that may increase an older man's risk of being neglected when his needs for support increase. Many men are not functioning in a kinkeeper role and are not attempting to repair fractured relationships. Minimizing their own feelings may prevent men from understanding the extent of alienation felt by an adult child.     

The Experience-Earnings Profile: Productivity-Augmenting or Purely Contractual? Evidence from the UK

We test the human capital interpretation of the experience-earnings profile. Does the upward sloping portion of the experience-earnings profile reflect on-the-job training which in turn causes the experience-productivity profile to slope upwards, or do purely contractual factors determine the nature of life-cycle earnings. Herein, we provide additional evidence on the relationship between productivity and earnings by examining earnings differentials in the UK academic labor market for economists. Using a test first suggested by Mincer, we find that the empirical results are consistent with human capital theory. We find that, although the positive relationship between earnings and experience persists when individual productivity measures are included in the salary equations for lecturers and senior lecturers, the positive relationship becomes statistically insignificant when the same productivity measures are included in the salary equations for professors. For lecturers and senior lecturers, the experience-salary profile properly reflects the structure of the national pay scale rather than variations in individual research productivity. At the professor level, where individual salaries are not determined by a pay scale, the data support the human capital explanation of the positive experience-earnings profile.

'The grit in the oyster': Community development workers in a modernizing local authority

This article offers a brief overview of the challenges facingUK local authorities, including the need to enhance public participationin decision making and service delivery, improve service performanceand increase partnership working. It explores the potentialcontribution of community development work to meeting thesechallenges, drawing on a case study of one UK county council.The essential tensions and conflicts in the role of communitydevelopment workers in a local authority are highlighted, showinghow the modernization process introduced by the New Labour governmentis adding further layers of complexity and ambiguity.     

Rurality and Income Inequality in the United States, 1975–2015

Recent events have focused attention on the perceived widening of the economic divide between urban and rural areas, and on the continued rise of national income inequality. We demonstrate that, in fact, the average income gap between urban (metropolitan) and rural (nonmetropolitan) households has not risen over the past 40 years, and makes virtually no contribution to national income inequality. Rising national inequality is driven by rising inequality within both urban and rural America, not by an urban/rural divergence. As is well known, the growing dispersion of household money income is partly driven by rising wage inequality, particularly in urban areas. Less well recognized is the role played by other income sources. We show that a decline in the progressivity of the distribution of social security payments and cash transfers, and an increase in the regressivity of the distribution of retirement incomes, have jointly made a comparably large contribution to rising income inequality. At the same time, the share of income from self-employment has declined, particularly in rural America, and because self-employment income is very unequally distributed, its diminution has retarded the growth of rural inequality. In 2014–15, however, rural inequality increased, cutting the urban/rural inequality gap in half.     

Infant screen exposure links to toddlers' inhibition,but not other EF constructs: A propensity score study

Technology is pervasive in homes of families with young children, despite evidence for negative associations between infant exposure to screen‐based media and cognitive development that has led the American Academy of Pediatrics (AAP) to discourage parents from exposing children under the age of 18 months to any kind of screen time (AAP, 2016). Here, we apply a propensity score matching approach to estimate relations between electronic screen‐based media use in infancy and executive function in early toddlerhood. In an international sample of 416 firstborn infants, parental report of regular exposure to screen‐based media at 4 months predicted poorer performance on a test of inhibition at 14 months, but was unrelated to either cognitive flexibility or working memory at 14 months. Results of this study are therefore consistent with the view that early exposure to screen‐based media adversely affects the development of executive function.