Decomposition of Scatter Ratios Used in Monitoring Multivariate Process Variability

Wilks’ ratio statistic can be defined in terms of the ratio of the sample generalized variances of two non-independent estimators of the same covariance matrix. Recently this statistic has been proposed as a control statistic for monitoring changes in the covariance matrix of a multivariate normal process in a Phase II situation, particularly when the dimension is larger than the sample size. In this article we derive a technique for decomposing Wilks’ ratio statistic into the product of independent factors that can be associated with the components of the covariance matrix. With these results, we demonstrate that, when a signal is detected in a control procedure for the Phase II monitoring of process variability using the ratio statistic, the signaling value can be decomposed and the process variables contributing to the signal can be specifically identified.     

Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.     

Re-examining two tests for bivariate normality

Many goodness of fit tests for bivariate normality are not rigorous procedures because the distributions of the proposed statistics are unknown or too difficult to manipulate. Two familiar examples are the ring test and the line test. In both tests the statistic utilized generally is approximated by a chi-square distribution rather than compared to its known beta distribution. These two procedures are re-examined and re-evaluated in this paper. It is shown that the chi-square approximation can be too conservative and can lead to unnecessary

rejection of normality.     

Correlation-Type Goodness of Fit Test for Extreme Value Distribution Based on Simultaneous Closeness

In reliability studies, one typically would assume a lifetime distribution for the units under study and then carry out the required analysis. One popular choice for the lifetime distribution is the family of two-parameter Weibull distributions (with scale and shape parameters) which, through a logarithmic transformation, can be transformed to the family of two-parameter extreme value distributions (with location and scale parameters). In carrying out a parametric analysis of this type, it is highly desirable to be able to test the validity of such a model assumption. A basic tool that is useful for this purpose is a quantile–quantile (QQ) plot, but in its use, the issue of the choice of plotting position arises. Here, by adopting the optimal plotting points based on Pitman closeness criterion proposed recently by Balakrishnan et al. (2010b Balakrishnan , N. , Davies , K. F. , Keating , J. P. , Mason , R. L. ( 2010b ). Computation of optimal plotting points based on Pitman Closeness with an application to goodness of fit for location-scale families. Submitted to Computational Statistics & Data Analysis.  [Google Scholar]), and referred to as simultaneous closeness probability (SCP) plotting points, we propose a correlation-type goodness of fit test for the extreme value distribution. We compute the SCP plotting points for various sample sizes and use them to determine the mean, standard deviation and critical values for the proposed correlation-type test statistic. Using these critical values, we carry out a power study, similar to the one carried out by Kinnison (1989 Kinnison , R. ( 1989 ). Correlation coefficient goodness of fit test for extreme value distribution . The American Statistician 43 : 98 – 100 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), through which we demonstrate that the use of SCP plotting points results in better power than with the use of mean ranks as plotting points and nearly the same power as with the use of median ranks. We then demonstrate the use of the SCP plotting points and the associated correlation-type test for Weibull analysis with an illustrative example. Finally, for the sake of comparison, we also adapt two statistics proposed by Gan and Koehler (1990 Gan , F. F. , Koehler , K. J. ( 1990 ). Goodness of fit based on P-P probability plots . Technometrics 32 : 289 – 303 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), in the context of probability–probability (PP) plots, based on SCP plotting points and compare their performance to those based on mean ranks. The empirical study also reveals that the tests from the QQ plot have better power than those from the PP plot.     

Research on Marital Satisfaction and Stability in the 2010s: Challenging Conventional Wisdom

Although getting married is no longer a requirement for social acceptance, most people do marry in their lifetimes, and couples across the socioeconomic spectrum wish their marriages to be satisfying and long lasting. This review evaluates the past decade of research on the determinants of satisfaction and stability in marriage, concluding that the scholarship of the past 10 years has undermined three assumptions that were formerly accepted as conventional wisdom. First, research exploiting methods such as latent class growth analyses reveal that, for most couples, marital satisfaction does not decline over time but in fact remains relatively stable for long periods. Second, contrary to predictions of behavioral models of marriage, negative communication between spouses can be difficult to change, does not necessarily lead to more satisfying relationships when it is changed, and does not always predict distress in the first place. Third, dyadic processes that are reliably adaptive for middle-class and more affluent couples may operate differently in lower income couples, suggesting that influential models of marriage may not generalize to couples living in diverse environments. Thus, the accumulated research of the past 10 years indicates that the tasks of understanding and promoting marital satisfaction and stability are more complex than we appreciated at the start of the decade, raising important questions that beg to be answered in the years ahead.     

Weighted Approximations to Continuous Time Martingales with Applications

A weighted approximation to a sequence of continuous time martingales by a time transformed Wiener process is established. The basic tool of proof is the Skorohod imbedding for martingale difference sequences. As an application of the main result a useful weighted approximation to the randomly weighted uniform empirical process is derived. A number of other applications are also discussed.     

Too old to test? Prevalence and correlates of HIV testing among sexually active older adults

ABSTRACT

Older adults account for 17% of new HIV diagnoses in the US and are more likely to be diagnosed with HIV later in the course of the disease compared to younger people. We calculated the prevalence and associated factors of having ever been tested for HIV among sexually active older adults. We analyzed data from the 2008–2016 General Social Survey Limited to respondents ≥65 years of age who reported more than one sex partner(s) in past 12 months (n = 757). HIV testing prevalence, prevalence ratios, and 95% confidence intervals were calculated by demographic variables and HIV-related risk behaviors. An estimated 16.3% of sexually active older adults have tested for HIV, and 15.9% were at increased risk for HIV infection (reported injection drug and/or crack–cocaine use, exchanging money for sex, more than three sex partners in the past year, or men who reported having sex with another man). In the adjusted model, adults aged 65–70, not married, self-identified as gay/bisexual, and at increased risk for HIV infection were more likely to have tested for HIV. An estimated 83.7% of sexually active older adults never tested for HIV. Strategies are needed to increase HIV awareness and testing among potentially high-risk older adults.     

Preparing for Social Work Practice in Diverse Contexts: Introducing an Integrated Model for Class Discussion

Understanding the context of practice is an essential component of social work practice as is providing service that respects diversity. These twin concepts are necessary to include in planning and delivering services across all levels of practice. However, while we might understand how the context impacts on service users (and such an understanding is a vital part of assessment processes), the context has greater and more far reaching impacts. For example, in rural practice research, there is evidence that the context strongly influences the choice of practice methods, the behaviour of the professional as an individual and as a community member, and the management of complex ethical situations. This paper proposes a model that may be useful in analysing the various impacts of diversity and context in social work practice, and is relevant for the education of social workers and other human service personnel. The SUPAmodel (Service User, Professional, Agency) uses practice examples to explore how changes in context impact on professional decision making and choices about intervention.