Statistics Problems with Simple Numbers

This article concerns the construction of simple numerical illustrations of statistical techniques for use in introductory classes. Minimizing the amount of calculation facilitates checking, promotes reliability, is quicker, and reinforces the confidence of the student. Methods are described for generating (a) samples of size 3 upwards with integer-valued means and standard deviations, and (b) simple linear regressions with integer-valued intercepts and integer-valued or simple fractional slopes. Extensions to give exact pooled standard deviations in the two-sample problem and simple exact fractional correlation coefficients are also indicated. Further statistical procedures amenable to the same general approach are listed.     

A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.     

Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

Number of observations near the maximum in an F α-scheme

Let K _n (a) be the number of observations in the interval (M _n ,?a, M _n ), where M _n is the maximum value in a sequence of size n. We study the asymptotic properties of K _n (a) under the F ^α-scheme and discuss the influence of the associated sequence α _n on the limit behaviour of this random variable.     

ISO 45001 and controversial transnational private regulation for occupational health and safety

This article analyses the genesis of the ISO 45001 standard on occupational health and safety, a new initiative of transnational private regulation. The authors draw a picture of controversy from interviews with stakeholders involved in its design, approval and initial dissemination, and from a qualitative content analysis of the internal documentation of the committee responsible for its approval. Like its predecessors relating to environmental management – ISO 14001 – and corporate social responsibility – ISO 26000 – this new standard raises serious concerns among stakeholders given that it deals with substantive political, social and legal issues.     

Mixed Messages: Inconsistent Parental Mediation Indirectly Predicts Teens’ Online Relational Aggression

Although the predictors of off-line relational aggression have been examined in prior work, less is known about the factors that contribute to online relational aggression perpetration and victimization. This study examined parental restrictive and active mediation of teenagers’ social media use as potential predictors of these outcomes. We were particularly interested in understanding whether parental agreement about media rules and the consistency with which mediation was implemented had implications for teens’ social media use, conflict with parents, and experience with online relational aggression. We conducted an online survey of 814 adolescents from the United States (14- to17-year-olds), asking about perceived agreement between parents about media rules, parental mediation styles, the teens’ social media use, and their experiences with online relational aggression. Results showed that parental rule agreement negatively predicted inconsistent parental mediation. Inconsistent parental mediation predicted more adolescent social media use and more parent-teen conflict over media rules, which in turn, predicted both online victimization and perpetration.     

The Women’s Empowerment in Livestock Index

Social Indicators Research - The empowerment of women in the livestock sector is fundamental to achieve gender equality. It also is instrumental for increased household productivity and improved...     

Constructing quantitative implementation scales from categorical services data. Examples from a multisite evaluation

Like measures of outcome, measures of implementation are most useful and analytically powerful when measured at client-level and are quantitative. However, high-quality, individual-level, quantitative service utilization data can be expensive, intrusive, or otherwise impractical to obtain. Cruder data--for example, presence versus absence of a given service--are often more feasible to collect, as well as more likely to be available. Consequently, evaluators can benefit by finding ways to better exploit such data at the analysis phase to compensate for shortcomings at the collection phase. This article documents one such instance in which this was done. Specifically, it describes how quantitative, client-level implementation scales were derived from qualitative (categorical) data and used to support a cross-site synthesis of implementation and outcome analyses in a multisite evaluation. It also suggests additional scenarios in which quantitative implementation scales might be derived form qualitative services data.