In the branch of probability called "large deviations," rates of convergence (e.g. of the sample mean) are considered. The theory makes use of the moment generating function. So, particularly for sums of independent and identically distributed random variables, the theory can be made accessible to senior undergraduates after a first course in…

What makes some explanations better than others? This paper explores the roles of simplicity and probability in evaluating competing causal explanations. Four experiments investigate the hypothesis that simpler explanations are judged both better and more likely to be true. In all experiments, simplicity is quantified as the number of causes…

In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use…

The thermodynamic concepts of First and Second Laws with respect to the entropy function are described using atoms and molecules and probability as manifested in statistical mechanics. The First Law is conceptually understood as [Delta]U = Q + W and the Second Law of Thermodynamics and the entropy function have provided the probability and…

This article engages students in a simulation of the Coat Check problem, in which four women check their coats only to have them returned at random. Students examine the experimental and theoretical probability of at least one woman getting her own coat back.

Previous methodological and applied studies that used binary logistic regression (LR) for detection of differential item functioning (DIF) in dichotomously scored items either did not report an effect size or did not employ several useful measures of DIF magnitude derived from the LR model. Equations are provided for these effect size indices.…

The existence of recurrent synaptic connections in CA3 led to the hypothesis that CA3 is an autoassociative network similar to the Hopfield networks studied by theorists. CA3 undergoes gamma frequency periodic inhibition that prevents a persistent attractor state. This argues against the analogy to Hopfield nets, in which an attractor state can be…

The Monty Hall three-door, "Let's Make a Deal" game, named after the 1970s television show, is used widely in economics, econometrics, statistics, and game-theory-based teaching, as well as in many other disciplines. Its solutions and underlying assumptions arouse great passion and argument, in both the academic and popular press. Most economists…

Alternative measures of "confirmation" or "evidential support" have been proposed to express the impact of ascertaining one event on the credibility of another. We report an experiment that compares the adequacy of several such measures as descriptions of confirmation judgment in a probabilistic context.

A logit model predicting student outcomes for a gateway course, Math for Liberal Arts, was successfully developed which fits the data well. Two variables, ACT math score and high school GPA, were found to be significant predictors of achieving a C or better in Math for Liberal Arts. A practical implication of the study suggests that with just two…

Using data from the Youth in Transition Survey (YITS), this paper provides an up-to-date description of educational and labour market pathways (or transitions) among Canadian youth. It also estimates the effect of academic abilities, measured by PISA math and reading scores, on such transitions. Descriptive statistics show that educational success…

This Technical Brief presents an historical analysis of key indicators of dropout for Delaware students in grades 9-12. Cut points for key risk indicators of high school dropout for the State of Delaware are provided. Using data provided by the Delaware Department of Education (DDOE), relationships between student dropout and several student…

The National Council of Teachers of Mathematics has set ambitious goals for the teaching and learning of mathematics that include preparing students for both the workplace and higher education. While this suggests that it is important for students to develop strong mathematical competencies by the end of high school, there is evidence to indicate…

This paper addresses a key methodological challenge in the modeling of individual poverty dynamics--the influence of measurement error. Taking the US and Britain as case studies and building on recent research that uses latent Markov models to reduce bias, we examine how measurement error can affect a range of important poverty estimates. Our data…

The following study describes design research in an elementary school near the metropolitan D.C. area with a diverse student population. The goal of the project was to design tasks that leveraged technology and enhance the access to critical thinking in specific mathematical concepts: data analysis and probability. It highlights the opportunities…