On the Test of Significance of Linear Multiple Regression Coefficients

The t-statistic used in the existing literature for testing the significance of linear multiple regression coefficients has only a limited use in testing the marginal significance of explanatory variables though it is used in testing the partial significance also. This article identifies the t-statistic appropriate for testing the partial significance.     

Distribution of the Activity Time in Network Analysis: A Critical Revisit with a Gamma Alternative

Network analysis is an important technique for project management. However, the current literature is biased toward beta distribution for modeling activity times. In this article, we have critically examined the role of beta distribution. It has been shown that beta distribution plays no specific role. Further, the method for calculating the chance of project completion must be revised. We have accordingly suggested an alternative modeling in terms of gamma distribution and proposed how to calculate the chance of project completion by taking into consideration both critical and noncritical paths. For demonstration purposes, we have considered a small project.     

Children living with parental substance misuse: A cross‐sectional profile of children and families referred to children's social care

Parental substance misuse is a significant public health and children's rights issue. In the United Kingdom, social workers frequently work with children and families affected by substance misuse. However, relatively little is known about this population, particularly at point of referral to children's social care. This paper reports on the largest known study of parental substance misuse as a feature of children's social care work in England. The paper provides a cross‐sectional profile of 299 children living with parental substance misuse and referred to children's social care in one local authority in England. Data were collected from social work case files at the point of referral to social care about the child, family, the wider environment, and parental substance misuse. The findings show that children affected by parental substance misuse frequently had other support needs relating to their well‐being and mental health. Children were also likely to be experiencing other parental and environmental risk factors. The significant historical—and in some cases intergenerational—social care involvement for some families indicates potential issues with the capacity of services to meet needs. Recommendations for practice are discussed with a particular focus on the need for early, comprehensive support for children and families.     

A Note on Determining Optimal Selling Price and Lot Size Under All-Unit Quantity Discounts

A recent study conducted by Abad [1] described a method of determining the optimal price and lot size when the supplier offers all-unit quantity discounts. The author developed a procedure using centralized and decentralized approaches. According to the author's suggestion, further study is necessary to determine if the decentralized approach always provides an optimal solution. In the present study, an attempt is made to investigate the uniformity between the centralized and decentralized approaches and to verify whether the decentralized approach always yields optimal solutions.     

An Inventory Model with Planned Shortages and Price Dependent Demand

Previous research has yielded a procedure for a retailer to determine the optimal lot size and selling price when a supplier offers all-unit quantity discounts and demand is a decreasing function of price. In this paper, we extend that research by allowing for shortages. An algorithm is presented that determines the optimal lot size, order level, and selling price for a class of demand functions, including the constant price-elasticity and linear demand functions.     

Parental substance misuse and statutory child protection in England: Risk factors and outcomes

Parental substance misuse is a significant child welfare issue and associated with increased risk of child maltreatment. The aim of the present study was to understand what social care outcomes children who live with parental substance misuse have, and to assess factors associated with those social care outcomes over a two-year period. The paper reports on a retrospective longitudinal study of 299 children all living with parental substance misuse and referred to one local authority in England. Data were collected from children's social work case files about procedural social care outcomes and factors which may be associated with those outcomes. Using cluster analysis, a new typology of children's longitudinal trajectories through the children's social care system was developed, consisting of five distinct types. Analysis indicated that some children received too little intervention from children's social care despite ongoing concerns, while other children were potentially unnecessarily caught up in the social care system. Factors associated with children having the poorest outcomes were: caregiver instability resulting from substance misuse, parenting capacity and household instability. The study's findings indicate that some children who live with parental substance misuse are at significant risk of harm, but others are not and may be better supported through non-statutory services such as early help.