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.     

Migration and mobility on the Amazon frontier

Migration patterns within tropical forest frontiers are highly complex and multidirectional, with movements to, from, and within these regions likely driven by different macro and micro factors. As such, several different conceptual models have been suggested to explain these dynamics. This paper uses data from a panel survey of households in a frontier region of the western Brazilian Amazon along with “second hand” reports on where people have moved to evaluate these conceptual models. Our rich data set, collected over nearly a decade from hundreds of households, allows us to compare households who arrived at different ages to assess predictions of the life cycle hypothesis; those who have been in the state (or on their properties) for different numbers of years to investigate the turnover hypothesis; those who arrived with different levels of capital to examine path dependence as suggested by conceptual models that focus on wealth dynamics; and the destination and purpose for moves from and within the study region to look for evidence of the frontier expansion hypothesis. We do not find any evidence for the turnover hypothesis, perhaps due to the favorable biophysical and market conditions in our study region. However, patterns in this region are consistent with all of the other conceptual models, reflecting the overlapping theoretical foundations of the models, and the complexity of migration and mobility on the frontier.     

Rape culture and social media: young critics and a feminist counterpublic

Social media sites, according to Carrie A. Rentschler, can become both “aggregators of online misogyny” as well as key spaces for feminist education and activism. They are spaces where “rape culture,” in particular, is both performed and resisted, and where a feminist counterpublic can be formed (Michael Salter 2013 Salter, Michael. 2013. “Justice and Revenge in Online Counter-Publics: Emerging Responses to Sexual Violence in the Age of Social Media.” Crime, Media, Culture: An International Journal 9 (3): 225–242.[Crossref], [Web of Science ®] , [Google Scholar]). In this New Zealand study, we interviewed seventeen young people who were critical of rape culture about their exposure and responses to it on social media and beyond. Participants described a “matrix of sexism” in which elements of rape culture formed a taken-for-granted backdrop to their everyday lives. They readily discussed examples they had witnessed, including victim-blaming, “slut-shaming,” rape jokes, the celebration of male sexual conquest, and demeaning sexualized representations of women. While participants described this material as distressing, they also described how online spaces offered inspiration, education, and solidarity that legitimated their discomfort with rape culture. Social media provided safe spaces that served as a buffer against the negative effects of sexism, and allowed participation in a feminist counterpublic that directly contests rape culture.     

High School Family Centers: Transformative Spaces Linking Schools and Families in Support of Student Learning

ABSTRACT

This study explores school, family, and community partnership at the high school level, using eight family centers as the entry point for the investigation. The purpose of the study was to identify ways that parents and school staff could collaborate to support high school students' achievement. The study findings led to the development of a model that represents three inputs that are crucial to the creation of a successful family center: (1) a supportive infrastructure, (2) the existence of skilled center staff, and (3) the presence of responsive programming. These three inputs led to the creation of a thriving center that acts as a transformative space, a “zone of community,” that results in four outputs: (1) the creation of relational trust among adults, (2) shift in parents' role construction and efficacy, (3) the generation of student relational trust, and (4) the development of student efficacy. The data from this study suggest that the relational trust developed in these transformative spaces called family centers can have a positive effect on student efficacy. The study concludes with seven recommendations for schools and districts looking to establish family centers in high schools as a way to expand family engagement at the high school level.