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…

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

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 note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

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.…

The authors present data from 2 feature verification experiments designed to determine whether distinctive features have a privileged status in the computation of word meaning. They use an attractor-based connectionist model of semantic memory to derive predictions for the experiments. Contrary to central predictions of the conceptual structure…

An objective method is presented to group discrete self-injurious behavior (SIB) events into bouts. Survival analysis was used to determine how long after an SIB the probability of observing a subsequent SIB remained elevated. This estimated bout length criterion time point was determined individually for 19 subjects with developmental disorders…

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a "transposition" of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic…