Statistical prediction remains an important tool for decisions in a variety of disciplines. An equally important issue is identifying factors that contribute to more or less accurate predictions. The time series literature includes well developed methods for studying predictability and volatility over time. This article develops…

This paper outlines the solution that the Team of Austria found to problem number 7, "skateboarder", presented in the finals of the 22nd International Young Physicists' Tournament (IYPT) in Tianjin, China. We investigated how a skateboarder can accelerate from rest on a horizontal surface without touching an external support. The focus was laid on…

Biology of the twenty-first century is an increasingly quantitative science. Undergraduate biology education therefore needs to provide opportunities for students to develop fluency in the tools and language of quantitative disciplines. Quantitative literacy (QL) is important for future scientists as well as for citizens, who need to interpret…

An examinee faced with a test item will engage in solution behavior or rapid-guessing behavior. These qualitatively different test-taking behaviors bias parameter estimates for item response models that do not control for such behavior. A mixture Rasch model with item response time components was proposed and evaluated through application to real…

The particular problem solved in this paper is that of calculating the time required to overtake a distant object receding under cosmic expansion, and the speed at which that object is passed. This is a rarely investigated problem leading to some interesting apparent paradoxes. We employ the problem to promote a deeper understanding of the dynamic…

This study tested whether 10- and 12-year-olds who can correctly compare the magnitudes of fractions with common components access the magnitudes of the whole fractions rather than only compare the magnitudes of their components. Time for comparing two fractions was predicted by the numerical distance between the whole fractions, suggesting an…

The "credit card effect" describes a finding where greater value is given to consumer items if credit card logos are present. One explanation for the effect is that credit cards elicit spending behavior through associative learning. If this is true, social, economic and historical contexts should alter this effect. In Experiment 1, Year…

Recently, Vul and Pashler (2008) demonstrated that the average of 2 responses from a single subject to general knowledge questions was more accurate than either single estimate. Importantly, this reveals that each guess contributes unique evidence relevant to the decision, contrary to views that eschew probabilistic representations of the…

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

Common source bias has been the focus of much attention. To minimize the problem, researchers have sometimes been advised to take measurements of predictors from one observer and measurements of outcomes from another observer or to use separate occasions of measurement. We propose that these efforts to eliminate biases due to common source…

Automated test assembly (ATA) has been an area of prolific psychometric research. Although ATA methodology is well developed for unidimensional models, its application alongside cognitive diagnosis models (CDMs) is a burgeoning topic. Two suggested procedures for combining ATA and CDMs are to maximize the cognitive diagnostic index and to use a…

A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The…

We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of first-order perturbation theory and show that it is greater than that for the case in which the nucleus is clamped…

Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear…