To participate or not to participate: that is the question

Do I wish to participate or not to participate in this program? That is the question that young people ask themselves when considering a new opportunity. What can be done to increase the likelihood that they will choose to participate in out-of-school-time (OST) programs? This chapter describes a qualitative study that examined reasons for participating or not participating in OST programs. Some common reasons emerged, but the study also revealed differences among youth from different ethnic groups. It is clear that those who design and conduct programs must understand the processes through which diverse adolescents initiate their participation in programs and either persist or drop out. Given the apparent benefits of active participation in youth programs, it is important to remove barriers and increase access and, equally important, design programs that are of interest to youth in the contexts in which they live.     

The effects of physical activity and sedentary behavior on cognitive health in older adults

Physical activity has been shown to be positively associated with cognitive health, but the mechanisms underlying the benefits of physical activity on cognitive health are unclear. The present study simultaneously examined two hypotheses using structural equation modeling (SEM). The depression-reduction hypothesis states that depression suppresses cognitive ability and that physical activity alleviates dysphoric mood and thereby improves cognitive ability. The social-stimulation hypothesis posits that social contact, which is often facilitated by socially laden physical activities, improves cognitive functioning by stimulating the nervous system. Sedentary behavior in the absence of physical activity is expected to exert an inverse relationship on cognitive health through each of these hypotheses. Community-dwelling elders (N = 158) were administered a variety of measures of cognition, depression, social support, and physical activity. SEM techniques provided partial support for the social-stimulation hypothesis and depression-reduction hypothesis. Implications for treating depression and improving cognitive functioning are discussed.     

Approximation of power in multivariate analysis

We consider the calculation of power functions in classical multivariate analysis. In this context, power can be expressed in terms of tail probabilities of certain noncentral distributions. The necessary noncentral distribution theory was developed between the 1940s and 1970s by a number of authors. However, tractable methods for calculating the relevant probabilities have been lacking. In this paper we present simple yet extremely accurate saddlepoint approximations to power functions associated with the following classical test statistics: the likelihood ratio statistic for testing the general linear hypothesis in MANOVA; the likelihood ratio statistic for testing block independence; and Bartlett's modified likelihood ratio statistic for testing equality of covariance matrices.     

Two Variations of the Minimum Steiner Problem

Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s S and t T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}–2,min {|S|,|T|}–1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|–2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.An extended abstract of part of this paper appears in Hsu et al. (1996).Supported in part by the National Science Foundation under Grants CCR-9309743 and INT-9207212, and by the Office of Naval Research under Grant No. N00014-93-1-0272.Supported in part by the National Science Council, Taiwan, ROC, under Grant No. NSC-83-0408-E-001-021.     

Relations Between Social Problem Solving and Indicators of Interpersonal and Family Well-Being Among Chinese Adolescents in Hong Kong

This study evaluated the dimensionality of the construct of social problem solving and examined the relationships between social problem solving and empathy, emotional well-being and family well-being in a sample of secondary school students in Hong Kong (N=1462). The participants completed measures of social problem solving (the 25-item short form of the Chinese version of the Social Problem-Solving Inventory: C-SPSI-R), empathy (the Chinese Interpersonal Reactivity Scale), emotional well-being (the Chinese Vengeance Scale) and family well-being (the Chinese Family Assessment Instrument and the Conflict Behaviour Questionnaire). Regarding the dimensionality of the C-SPSI, confirmatory factor analysis showed that the scale has a stable five-factor structure (RMSEA=0.05) and that the related subscales were reliable (with ranging from 0.65 to 0.81). Participants with higher levels of social problem solving had higher levels of empathy and lower personal distress in applying empathy, which suggested that these personal competencies were inter-related. Higher levels of social problem solving were also related to better emotional well-being (less tendency to take revenge) and better family quality of life (better family functioning and fewer parent-adolescent conflicts).     

A Factor Analytic Comparison of Ecological and Individual Correlations: Some Methodological Implications

Comparisons of factor analytic results based on a matrix of total (individual) correlations and three matrices of between-groups (ecological) correlations revealed fundamental differences in factor patterns when the unit of analysis shifted from individuals to aggregates. The major difference involved the marked tendency for a highly individualistic General Ability Factor derived from the matrix of total correlations to become more and more sociological in content as individuals were aggregated. Results are discussed in terms of their bearing on the problem of determining the "appropriateness" of a given unit of analysis, individuals vs. aggregates, for certain levels of inquiry, i.e., psychological vs. sociological. It is concluded that whether the researcher should heed the traditional warning about the use of aggregate data relationships as a basis for making inferences concerning individuals ought to depend in part on whether his interest is in psychological or sociological propositions about indivduals.     

Information in experiments and sufficiency

We define measures of information contained in an experiment which are by-products of the parametric measures of Fisher, Vajda, Mathai and Boekee and the non-parametric measures of Bhattacharyya, Rényi, Matusita, Kagan and Csiszár. We use these measures to compare sufficient experiments according to Blackwell's definition. In particular, we prove that if δ_X and δ_Y are two experiments and δ_X≥δ_Y then l_X≥l_y for all of the above measures.