Bertrand's paradox (Bertrand 1889 "Calcul des Probabilites" (Paris: Gauthier-Villars)) can be considered as a cautionary memento, to practitioners and students of probability calculus alike, of the possible ambiguous meaning of the term "at random" when the sample space of events is continuous. It deals with the existence of different possible…

This paper is an elementary introduction to particle diffusion in a medium where the coefficient of diffusion varies with position. The introduction is aimed at third-year university courses. We start from a simple model of particles hopping on a discrete lattice, in one or more dimensions, and then take the continuous-space limit so as to obtain…

The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing…

Birnbaum raised important challenges to testing transitivity. We summarize why an approach based on counting response patterns does not solve these challenges. Foremost, we show why parsimonious tests of transitivity require at least 5 choice alternatives. While the approach of Regenwetter, Dana, and Davis-Stober achieves high power with modest…

In this paper we seek to empirically quantify the role of peer social networks in influencing sexual behavior among adolescents. Using data of a nationally representative sample of adolescents we utilize a multivariate structural model with school-level fixed effects to account for the problems of contextual effects, correlated effects and peer…

The goal of this research was to disentangle effects of phonotactic probability, the likelihood of occurrence of a sound sequence, and neighbourhood density, the number of phonologically similar words, in lexical acquisition. Two-word learning experiments were conducted with 4-year-old children. Experiment 1 manipulated phonotactic probability…

Steinley and Brusco (2011) presented the results of a huge simulation study aimed at evaluating cluster recovery of mixture model clustering (MMC) both for the situation where the number of clusters is known and is unknown. They derived rather strong conclusions on the basis of this study, especially with regard to the good performance of…

With the rapid development of Internet technologies, distance education has become a popular educational mode. In this paper, the authors propose an online image automatic annotation distance education system, which could effectively help children learn interrelations between image content and corresponding keywords. Image automatic annotation is…

This paper considers the determinants of student participation in Michigan's large inter-district open enrollment system, known as Schools of Choice (SoC). Employing a rich dataset from the Michigan Department of Education, we examine the population of public school students in resident and non-resident school districts between the 2005-06 and…

The challenge of retaining teachers in the profession of agricultural education is a prevalent and growing problem in the United States. The purpose of this study was to determine the primary factors contributing to intention to leave the profession among Georgia agriculture teachers. Teacher-participants responded to a web-based survey which…

This article by Elizabeth Reeve and Kim Beswick illustrates how primary children may engage with the Statistics and Probability content contained in the Australian Curriculum. Technology has opened up many possibilities for young children to engage with statistics. In the process the children learned a great deal more than just mathematics.

The purpose of the current investigation was to develop and provide initial validation of the "Social and Academic Behavior Risk Screener" (SABRS). Research was conducted in southeast elementary schools with 54 teacher and 243 student participants. An initial item pool was created through review of developmental research on the…

In this study, we examine the development of student engagement in relation to dropout. We focus on different growth trajectories of engagement between groups of students and on whether these trajectories lead to differences in the survival of the student. The development of behavioural and emotional engagement of 4063 graduates and 541 (11.7%)…

The debate about whether making a risky choice is based on a weighting and adding process has a long history and is still unresolved. To address this long-standing controversy, we developed a comparative paradigm. Participants' eye movements in 2 risky choice tasks that required participants to choose between risky options in single-play and…

The Advanced Placement Program® (AP®) was created to provide access to rigorous, college-level curricula to motivated and prepared high school students. This study evaluated whether the AP Exam scores from the summative exams associated with 10 courses were valid for the placement of students into higher-level college courses in the subject area…