A multivariate projection‐type analogue of the Wilcoxon — Mann — Whitney test

The problem of comparing two independent groups based on mulitivariate data is considered. Many such methods have been proposed, but it is difficult to gain a perspective on the extent to which the groups differ. The basic strategy here is to determine a robust measure of location for each group, project the data onto the line connecting these measures of location, and then compare the groups based on the ordering of the projected points. In the univariate case the method uses the same measure of effect size employed by the Wilcoxon — Mann — Whitney test. Under general conditions, the projected points are dependent, causing difficulties when testing hypotheses. Two methods are found to be effective when trying to avoid Type I error probabilities above the nominal level. The relative merits of the two methods are discussed. The projected data provide not only a useful (numerical) measure of effect size, but also a graphical indication of the extent to which groups differ.     

Bradley — Terry — Luce models to incorporate within‐pair order effects: Representation and uniqueness theorems

The paper presents different representation theorems for the Bradley — Terry — Luce (BTL) models of Beaver and Gokhale and of Davidson and Beaver. In particular, algorithms that can be used in constructing BTL scales are provided. The uniqueness theorems show that the Davidson — Beaver model should be preferred to the Beaver — Gokhale model since the multiplicative order effect parameter is uniquely determined whereas the additive effect parameter is merely a ratio scale. Finally, a relationship to the simple BTL model is established. Let p(a, b) denote the probability that a is chosen when (a, b) is presented in a fixed order. Then the probabilities p(a, b) satisfy the Beaver — Gokhale model if and only if the balanced probabilities p_b(a, b):= ½ (p(a, b) + 1–p (b, a)) satisfy the simple BTL model.     

Re‐building Bridges: Homeless People's Views on the Role of Vocational and Educational Activities in Their Everyday Lives

Homeless people face everyday challenges of marginalisation and stigmatisation. Consequently, they can suffer from low self‐confidence, self‐efficacy and agency. Empirical research in Britain on educational, skill‐building and meaningful activities for homeless people principally emphasises the instrumental value of training and learning as a route to employment rather than the impact of activities on homeless people's everyday lives. Theoretical literature suggests that psychosocial benefits related to the development of self‐efficacy, agency and empowerment can be gained from such activities. Participants' experiences and perceptions of educational and recreational activities were examined through 29 interviews at three homeless day centres in London. Thematic analysis suggests the restorative power of engagement in activities and shows that participants value activities, not only as the foundation for future goals of finding employment and housing, but as an immediate way of restoring a sense of self and finding positive experiences with a focus on the present. The findings underline the importance of viewing these interventions from a ‘bottom‐up’ perspective. The study tentatively concludes that accepting and emphasising the immediate personal benefits as a positive achievement of activities may be a valuable approach to better engage homeless clients. Copyright © 2015 John Wiley & Sons, Ltd.