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…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

Multilevel modeling is an increasingly popular technique for analyzing hierarchical data. This article addresses the problem of predicting a future observable y[subscript *j] in the jth group of a hierarchical data set. Three prediction rules are considered and several analytical results on the relative performance of these prediction rules are…

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.