In multilevel modeling, group-level variables (L2) for assessing contextual effects are frequently generated by aggregating variables from a lower level (L1). A major problem of contextual analyses in the social sciences is that there is no error-free measurement of constructs. In the present article, 2 types of error occurring in multilevel data…

The famous Birthday Problem is a staple in introductory probability texts and can be stated as follows: What is the probability that at least two persons from "n" randomly chosen persons have the same birthday? In this article, the author suggests an adaptation of the birthday problem which can be repeated in class until the full effect…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

Digital systems offer computational power and instant feedback. Game designers are using these features to create scaffolding tools to reduce player frustration. However, researchers are finding some unexpected effects of scaffolding on strategy development and problem-solving behaviors. We used a digital Sudoku game named "Professor Sudoku" to…

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to…

Interest in testing interaction terms within the latent variable modeling framework has been on the rise in recent years. However, little is known about the influence of nonnormality and model misspecification on such models that involve latent variable interactions. The authors used Mattson's data generation method to control for latent variable…

VSEPR is a topic that is commonly taught in undergraduate chemistry courses. The readily available Web-based program WebMO, in conjunction with the computational chemistry programs MOPAC and GAMESS, is used to quantitatively test a wide range of predictions of VSEPR. These predictions refer to the point group of the molecule, including the…

In this article we propose several modeling choices to extend propensity score analysis to clustered data. We describe different possible model specifications for estimation of the propensity score: single-level model, fixed effects model, and two random effects models. We also consider both conditioning within clusters and conditioning across…

Relatively few undergraduate physical chemistry programs integrate molecular modeling into their quantum mechanics curriculum owing to concerns about limited access to computational facilities, the cost of software, and concerns about increasing the course material. However, modeling exercises can be integrated into an undergraduate course at a…

A general chemistry laboratory experiment is described that introduces students to instrumental analysis using gas chromatography-mass spectrometry (GC-MS), while simultaneously reinforcing the concepts of mass percent and the calculation of atomic mass. Working in small groups, students use the GC to separate and quantify the percent composition…

DETECT is a nonparametric methodology to identify the dimensional structure underlying test data. The associated DETECT index, "D[subscript max]," denotes the degree of multidimensionality in data. Conditional covariances (CCOV) are the building blocks of this index. In specifying population CCOVs, the latent test composite [theta][subscript TT]…

Recent studies have revealed a relation between the given response and the response latency for personality questionnaire items in the form of an inverted-U effect, which has been interpreted in light of schema-driven behavior. In general, more probable responses are given faster. In the present study, the relationship between the probability of…

In this laboratory experiment, students quantitatively determine the concentration of an element (mercury) in an environmental or biological sample while comparing and contrasting the fundamental techniques of atomic absorption spectrometry (AAS) and atomic fluorescence spectrometry (AFS). A mercury analyzer based on sample combustion,…

A marginal maximum a posteriori (MMAP) procedure was implemented to estimate item parameters in the generalized graded unfolding model (GGUM). Estimates from the MMAP method were compared with those derived from marginal maximum likelihood (MML) and Markov chain Monte Carlo (MCMC) procedures in a recovery simulation that varied sample size,…