To meet the requirements of the No Child Left Behind Act, school districts and states must compile summary reports of the levels of student achievement in reading and mathematics. The levels are to be described in broad categories: "basic and below," "proficient," or "advanced." Educational units are given considerable latitude in defining the…

Probability coverage for eight different confidence intervals (CIs) of measures of effect size (ES) in a two-level repeated measures design was investigated. The CIs and measures of ES differed with regard to whether they used least squares or robust estimates of central tendency and variability, whether the end critical points of the interval…

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example…

This study describes a method for incorporating external estimates of intraclass correlation to improve the precision for the analysis of an existing group-randomized trial. The authors use a random-effects meta-analytic approach to pool the information across studies, which takes into account any interstudy heterogeneity that may exist. This…

The purpose of this study was to identify selected factors related to annual fundraising program contributions at National Collegiate Athletic Association (NCAA) Division I-A (D I-A) institutions and develop an equation for estimating an annual fund-raising goal. Based on a review of the literature, 15 potential predictor variables were selected…

The tetrachoric correlation describes the linear relation between two continuous variables that have each been measured on a dichotomous scale. The treatment of the point estimate, standard error, interval estimate, and sample size requirement for the tetrachoric correlation is cursory and incomplete in modern psychometric and behavioral…

Large numbers of rural districts have experienced sharp declines in enrollment, unlike their suburban counterparts. Accurate enrollment projections are required, whether a district needs to build new schools or consolidate existing ones. For school districts having more than 600 students, a quantitative method such as the Cohort-Survival Ratio…

This study used kernel-smoothing procedures to estimate the item characteristic functions (ICFs) of a set of continuous personality items. The nonparametric ICFs were compared with the ICFs estimated (a) by the linear model and (b) by Samejima's continuous-response model. The study was based on a conditioned approach and used an error-in-variables…

This article explores the uses of a simulation model (the two bucket story)--implemented by a stand-alone computer program, or an Excel workbook (both on the web)--that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides…

The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

A structure for learning the connections among standard deviations, z-scores, and normal distributions is presented. The components of this structure are classified into intuitive or previously learned conceptual knowledge, computational knowledge, and formalized conceptual knowledge. (Contains 1 figure.)

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…

In textbook treatments of enzyme inhibition kinetics, adjustment of the initial inhibitor concentration for inhibitor bound to enzyme is often neglected. For example, in graphical plots such as the Dixon plot for estimation of an inhibition constant, the initial concentration of inhibitor is usually plotted instead of the true inhibitor…

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…