The mathematics of Benford’s law: a primer

This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid researchers who are interested in applying Benford’s law, and need to understand general principles clarifying when to expect the appearance of Benford’s law in real-life data and when not to expect it. A second main target audience is students of statistics or mathematics, at all levels, who are curious about the mathematics underlying this surprising and robust phenomenon, and may wish to delve more deeply into the subject. This survey of the fundamental principles behind Benford’s law includes many basic examples and theorems, but does not include the proofs or the most general statements of the theorems; rather it provides precise references where both may be found.

     

The Family Unpredictability Scale: Reliability and Validity

We developed the Family Unpredictability Scale (FUS) to better understand the factors that underlie the presence and consequences of family dysfunction. Familial unpredictability is defined as a lack of consistency in family behaviors and regulatory systems. Family researchers and therapists generated and evaluated items, which were self‐administered by married parents who had children aged 2 to 18 (N= 314 ). Principal‐components analysis yielded four subscales (discipline, nurturance, meals, and money; 22 items total) that were internally consistent; confirmatory factor analysis based on a separate subsample yielded an adequate preliminary representation of this factor structure. The FUS related significantly to known measures of family and individual functioning but not to social desirability. The present study provides preliminary reliability, construct validity, and concurrent validity for this new multidimensional, self‐report assessment of family unpredictability. Research and clinical implications are discussed.     

Beyond Social Constructionism: Critical Realism and Social Work

Summary Theories within the social and psychological sciences continueto shape social work practice. However, recent debates withinthese sciences on the shortcomings of ‘social constructionism’,and the attempt to overcome them through a critical realistposition, have so far failed to capture social work's attention.This paper provides a critical overview of these theoreticaldebates, highlighting the shortcomings of social constructionismfor social work. The critical realist challenge to social constructionism,as articulated by the British philosopher Roy Bhaskar, is consideredand its relevance to social work formulated in terms of a returnto ‘depth’ in practice.     

Developing creative solutions to the problems of children and their families: communicative reason and the use of forum theatre

The paper represents a further development of work previously reported in this journal by Spratt & Houston (1999) and Spratt et al. (2000) . The authors have sought to develop ways of understanding current social work with children and families in line with the critical theory of Jurgen Habermas. This analysis has been complemented by an adoption of the methodology of the radical dramatist, Augusto Boal. In synthesizing Habermas's analysis of communicative discourses with the consciousness raising methodology of Boal, the authors have already demonstrated the effectiveness of this hybrid in problem‐solving exercises with social workers. The present paper reports on an application of this developing theory to practice, utilizing the centrepiece of Boal's method, forum theatre. A forum theatre project, concerned with the issue of bullying, is described and evaluated. It is argued that the project provides an exemplar of an innovative, democratizing and effective methodology that might profitably be utilized in social work with children and families. Finally, suggestions are made as to how these ideas could be developed in practice.     

The demographic impact of Partition in the Punjab in 1947

We use data from the 1931, 1941, and 1951 censuses of India and the 1951 census of Pakistan to examine the demographic consequences of Partition in the Punjab in 1947. Had growth rates for the period 1931-41 for the Punjab as a whole continued to 1951, the population of the Punjab would have been 2.9 million larger than that recorded in 1951. Population losses from migration and mortality above age 20 were approximately 2.7 million greater between 1941 and 1951 than would have been predicted by loss rates between 1931 and 1941. We estimate a net Partition-related population movement out of the combined Punjab of about 400,000. We conclude from several lines of analysis that Partition-related population losses in the Punjab, either from deaths or unrecorded migration, were in the range 2.3-3.2 million. Partition was also marked by a dramatic religious homogenization at the district level.     

Moving and union dissolution

This paper examines the effect of migration and residential mobility on union dissolution among married and cohabiting couples. Moving is a stressful life event, and a large, multidisciplinary literature has shown that family migration often benefits one partner (usually the man) more than the other Even so, no study to date has examined the possible impact of within-nation geographical mobility on union dissolution. We base our longitudinal analysis on retrospective event-history data from Austria. Our results show that couples who move frequently have a significantly higher risk of union dissolution, and we suggest a variety of mechanisms that may explain this.     

Fitting Hierarchical Holographic Modeling into the Theory of Scenario Structuring and a Resulting Refinement to the Quantitative Definition of Risk

A point of view is suggested from which the Hierarchical Holographic Modeling (HHM) method can be seen as one more method within the Theory of Scenario Structuring (TSS), which is that part of Quantitative Risk Assessment having to do with the task of identifying the set of risk scenarios. Seen in this way, HHM brings strongly to our attention the fact that different methods within TSS can result in different sets of risk scenarios for the same underlying problem. Although this is not a problem practically, it is a bit awkward conceptually from the standpoint of the "set of triplets" definition of risk, in which the scenario set is part of the definition. Accordingly, the present article suggests a refinement to the set of triplets definition, which removes the specific set of scenarios, found by any of the TSS methods, from the definition of risk and casts it, instead, as an approximation to the "true" set of scenarios that is native to the problem at hand and not affected by the TSS method used.