A Bayesian method of sample size determination with practical applications

Summary.  The problem motivating the paper is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation-based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution that is used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non-informative prior distributions lead to very small sample sizes. In contrast, a very informative prior distribution may either lead to a very small or a very large sample size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods that are developed are quite general and can be applied to other sample size determination problems. Some numerical illustrations which bring out many other aspects of the optimum sample size are given.     

Nonprofit management education through distance learning

Course books 1–12 for “Managing Voluntary and Non-Profit Enterprises.” Milton Keynes, U.K.: The Open University, 1991. (For information, contact Open University Enterprises, 12 Coferidge Close, Stony Stratford, Milton Keynes, MK11 1BY, U.K.) Issues in Voluntary and Non-Profit Management: A Reader, edited by Julian Batsleer, Chris Cornforth, and Rob Paton. Workingham, England: Addison-Wesley, in association with The Open University, 1991. 215 pp., paper. Writers on Organizations (4th ed.), by D. S. Pugh and D. J. Hickson. London: Penguin Books, 1989. 201 pp., paper.     

Transfer programs and aggregate household formations

The number of households in the United States increased by over fifty percent in the 1960s and 1970s, nearly double the rate of population growth. Part of the increase is explained by the movement of large cohort groups of the population into prime household-forming age categories, but higher headship rates also contribute. Age-specific headship rate increases result from non-demographic factors, and this paper focuses on the role of government transfer payment programs. Specifically considered are Social Security, Aid to Families with Dependent Children, and Food Stamps. These programs are found to have accounted for as many as 4 million net household formations between 1961 and 1984. The findings have implications for expected households formations in the 1990s.     

Modelling the management of underground water assets

Central to the activities of any industry is the modernization of its assets. This paper describes the application of statistical methods to the asset management plan of a large water company. A model for the underground assets is given in detail, and the extensive computations required are illustrated. A Bayesian model shows the consequences of various policy options and provides realistic measures of the uncertainty connected with them.     

Parental mental health: disruptions to parenting and outcomes for children

The association between parental mental health problems and negative outcomes for children has been long known. This paper addresses three issues in relation to this. First, the scale of the problem is outlined, in terms of both the prevalence of mental health problems in parents and the likelihood of children exhibiting negative outcomes in these circumstances. Secondly, the specificity, or lack of it, of particular outcomes in the child in relation to different parental mental health problems is explored. Thirdly, the paper focuses on the importance of disruptions to parenting as a mechanism in the transmission of mental health problems to negative impacts on the child. Examples are given of how parenting is disrupted in non‐clinical community populations, and the subsequent impacts on the child. The case is made for the preventative importance of parenting and family support in mediating between parental mental health problems and negative impacts on the child.     

Higher order moments of order statistics from INID symmetric random variables

In this paper we present analogues of Balakrishnan's (1989) relations that relate the triple and quadruple moments of order statistics from independent and nonidentically distributed (I.NI.D.) random variables from a symmetric distribution to those of the folded distribution. We then apply these results, along with the corresponding recurrence relations for the exponential distribution derived recently by Childs (2003), to study the robustness of the Winsorized variance.     

The Spread of Disability Living Allowance

This article examines the spread of Disability Living Allowance across a group of low income households in an industrial town in North West England from the introduction of the new benefits in 1992 until the Spring of 1996. We focus on the changes over time of the incidence of Disability Living Allowance in the low income population and look at the relative spread of different elements of the benefit. We speculate on whether the new benefits have provided the most effective way of fulfilling the aims of the White Paper, The Way Ahead , and discuss the implications for social and medical models of disability.     

Parental reactions to developmental disabilities in Chinese American families

Families of Chinese American children with mental retardation and developmental disabilities were interviewed regarding their attitudes and coping experiences. Chinese American parents, like other American parents, reacted to the crisis with intense feelings and needs. The parents revealed a lack of knowledge and understanding of the diagnosis. Chinese belief systems about health and illness were present in the parents' concepts of causation and treatment.Hunter College School of Social Work.     

Religion and Giving in Australia

This article draws on a household survey of giving and volunteering undertaken as part of the Giving Australia project to explore the relationship between religion and the giving behaviour of adult Australians. We find that people who identify themselves as having a religion are more likely to give and to give more on average than people who do not but that this relationship is produced by a subset of this group; namely, people who regularly attend religious services. Indeed, the likelihood of giving and average amounts given by givers over a year increase with levels of attendance at religious services. The relationship holds even after allowing for other factors that affect the likelihood of a person giving and the amount given. It also holds for giving to nonreligious causes (ie when giving to religion is omitted). However, when we also omit giving to charities and look at giving to civic causes alone we find that the frequency of attendance at religious services has an ambiguous relationship with giving. A suggestion in overseas literature that it is participation in religious groups, rather than attendance at religious services that is associated with giving is not supported.