Both adults and young children possess powerful statistical computation capabilities--they can infer the referent of a word from highly ambiguous contexts involving many words and many referents by aggregating cross-situational statistical information across contexts. This ability has been explained by models of hypothesis testing and by models of…

We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…

This paper provides practical guidance for researchers who are designing and analyzing studies that randomize schools--which comprise three levels of clustering (students in classrooms in schools)--to measure intervention effects on student academic outcomes when information on the middle level (classrooms) is missing. This situation arises…

Consider a discrete bivariate random variable (X, Y) with possible values x[subscript 1], x[subscript 2],..., x[subscript I] for X and y[subscript 1], y[subscript 2],..., y[subscript J] for Y. Further suppose that the corresponding families of conditional distributions, for X given values of Y and of Y for given values of X are available. We…

In the framework of the Italian National Plan "Lauree Scientifiche" (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum…

We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…

We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the Siegert approximation, the complex scaling method and the box-stabilization method. A comparison of the…

Accurate time measurement is essential to temporal analysis in sport. This study aimed to (a) develop a new method for time computation from surveyed trajectories using a high-end global navigation satellite system (GNSS), (b) validate its precision by comparing GNSS with photocells, and (c) examine whether gate-to-gate times can provide more…

The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different…

Research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Many of these designs involve two levels of clustering or nesting (students within classes and classes within schools). Researchers would like to compute effect size indexes based on the standardized mean difference to…

Traditionally, the first mathematical task for primary grade students to master is addition. Mastering addition facts is truly a positive experience. Then one turns to subtraction. After mastering addition facts, many students think that subtraction facts are a whole new set of facts to learn that have nothing to do with addition facts. They do…

The interference fringes produced by a diffraction grating illuminated with radiation from a TV remote control and a red laser beam are, simultaneously, captured by a digital camera. Based on an image with two interference patterns, an estimate of the infrared radiation wavelength emitted by a TV remote control is made. (Contains 4 figures.)

Latent class analysis (LCA) is an increasingly popular tool that researchers can use to identify latent groups in the population underlying a sample of responses to categorical observed variables. LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when…

The root mean square error of approximation (RMSEA) is one of the most widely reported measures of misfit/fit in applications of structural equation modeling. When the RMSEA is of interest, so too should be the accompanying confidence interval. A narrow confidence interval reveals that the plausible parameter values are confined to a relatively…

The failures of previous studies to demonstrate productivity differences across different percentages of incentive pay may be partially due to insufficient simulation fidelity. The present study compared the effects of different percentages of incentive pay using a more advanced simulation method. Three payment methods were tested: hourly,…