This study investigated the development of children's knowledge of many-to-one counting. Four-year-olds ("n" = 51) either participated in a training or in a control group. The training taught children how to allot "Y" physically not present items to each of "X" objects and how to count these items in the process. It…

The Golden Ratio is sometimes called the "Golden Section" or the "Divine Proportion", in which three points: A, B, and C, divide a line in this proportion if AC/AB = AB/BC. "Donald in Mathmagicland" includes a section about the Golden Ratio and the ratios within a five-pointed star or pentagram. This article presents two computing exercises that…

M. Pena, L. L. Bonatti, M. Nespor, and J. Mehler (see record 2002-06215-001) argued that humans compute nonadjacent statistical relations among syllables in a continuous artificial speech stream to extract words, but they use other computations to determine the structural properties of words. Instead, when participants are familiarized with a…

L. L. Bonatti, M. Pena, M. Nespor, and J. Mehler (see record 2006-06642-010) argued that P. Perruchet, M. D. Tyler, N. Galland, and R. Peereman (see record 2004-21166-008) confused the notions of segmentation and generalization by ignoring the evidence for generalization in M. Pena, L. L. Bonatti, M. Nespor, and J. Mehler (see record…

Computational precision is sometimes given short shrift in a first programming course. Treating this topic requires discussing integer and floating-point number representations and inaccuracies that may result from their use. An example of a moderately simple programming problem from elementary statistics was examined. It forced students to…

A linear combination of a set of measures is often sought as an overall score summarizing subject performance. The weights in this composite can be selected to maximize its reliability or to maximize its validity, and the optimal choice of weights is in general not the same for these two optimality criteria. We explore several relationships…

Recently, economists have developed methods for structural estimation of auction models. Many researchers object to these methods because they find the strict rationality assumptions to be implausible. Using bid data from first-price auction experiments, we estimate four alternative structural models: (1) risk-neutral Bayes-Nash, (2) risk-averse…

The use of Bayes' formula is applied to the biological problem of pedigree analysis to show that the Bayes' formula and non-Bayesian or "classical" methods of probability calculation give different answers. First year college students of biology can be introduced to the Bayesian statistics.

A practical approach for familiarizing students with the thermodynamics of the inclusion phenomena is described. The experiment facilitates calculation of the activation parameters corresponding to the reactions involved in the inclusion mechanism.

This article reviews several basic statistical tools needed for modeling data with sampling weights that are implemented in Mplus Version 3. These tools are illustrated in simulation studies for several latent variable models including factor analysis with continuous and categorical indicators, latent class analysis, and growth models. The…

In applications of structural equation modeling, it is often desirable to obtain measures of uncertainty for special functions of model parameters. This article provides a didactic discussion of how a method widely used in applied statistics can be employed for approximate standard error and confidence interval evaluation of such functions. The…

The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…

We argue that to test preschoolers' understanding of counting, one has to use tasks that relate counting to the goal of doing arithmetic, as counting and arithmetic principles are mutually constrained. A naturalistic study in the preschool classroom led to the development of an ''arithmetic-counting'' task, where counting was being related to the…

The ubiquity of calculators led to many "computational abuses", when numbers substitute for substance. On the other hand, it resulted in decrease in number oriented dexterity of students. The latter led to a disdain for even simple calculations to work about unfamiliar mathematical problems. As a reaction to the former, the reputation of…

A type of data layout that may be considered as an extension of the two-way random effects analysis of variance is characterized and modeled based on group invariance. The data layout seems to be suitable for several scenarios in psychometrics, including the one in which multiple measurements are taken on each of a set of variables, and the…