A method for using electronic structure calculations to predict the standard molar enthalpy of combustion for hydrocarbons is presented. In this approach, simple geometry optimizations can be used to accurately compute the enthalpy of combustion within 3% of the experimental value using Hartree-Fock, MP2, or virtually any functional in density…

Financial analysts generally create static formulas for the computation of NPV. When they do so, however, it is not readily apparent how sensitive the value of NPV is to changes in multiple interdependent and interrelated variables. It is the aim of this paper to analyze this variability by employing a dynamic, visually graphic presentation using…

This article is designed to give the reader a conceptual, nontechnical overview of estimation and model fit issues in multilevel modeling (MLM). The process of MLM generally involves fitting a series of multilevel models that increase in complexity. When conducting multilevel analyses, it is important to balance the need for complexity and the…

Applied early adolescent researchers often sample students (Level 1) from within classrooms (Level 2) that are nested within schools (Level 3), resulting in data that requires multilevel modeling analysis to avoid Type 1 errors. Although several articles have been published to assist researchers with analyzing sample data nested at two levels, few…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This sixth installment of "Explorations in Statistics" explores correlation, a familiar technique that estimates the magnitude of a straight-line relationship between two variables. Correlation is meaningful only when the…

Interval estimation of intraclass correlation coefficients in hierarchical designs is discussed within a latent variable modeling framework. A method accomplishing this aim is outlined, which is applicable in two-level studies where participants (or generally lower-order units) are clustered within higher-order units. The procedure can also be…

The authors describe an activity they have created in which students can visualize a theoretical neural network whose states evolve according to a well-known simple law. This activity provided an uncomplicated approach to a paradigm commonly represented through complex mathematical formulation. From their observations, students learned many basic…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

Mediation analysis is a statistical approach used to examine how the effect of an independent variable on an outcome is transmitted through an intervening variable (mediator). In this article, we provide a gentle introduction to single-level and multilevel mediation analyses. Using single-level data, we demonstrate an application of structural…

This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a…

A new effect size representing the predictive power of an independent variable from a multiple regression model is presented. The index, denoted as r[subscript sp], is the semipartial correlation of the predictor with the outcome of interest. This effect size can be computed when multiple predictor variables are included in the regression model…

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

This methodological note illustrates how a commonly used calculation of the Delta-p statistic is inappropriate for categorical independent variables, and this note provides users of logistic regression with a revised calculation of the Delta-p statistic that is more meaningful when studying the differences in the predicted probability of an…

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to "think aloud" so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are…

In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by…