The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing…

In this exercise, students apply a combination of techniques to investigate the impact of metal identity and ligand field strength on the spin states of three d[superscript 5] transition-metal complexes: Fe(acac)[subscript 3], K[subscript 3][Fe(CN)[subscript 6]], and Ru(acac)[subscript 3], where acac[superscript -] is acetylacetonate. Students…

Formula unit (or molecular) volume, "V[subscript m]", is related to many thermodynamic and physical properties of materials, so that knowledge of "V[subscript m]" is useful in prediction of such properties for known and even hypothetical materials. The symbol "Z" represents the number of formula units in a crystallographic unit cell; "Z" thus…

Around 240 B.C., Eratosthenes made what is considered to be the most famous and accurate of the ancient measurements of the circumference of the Earth. It was accomplished by making "presumably simultaneous" measurements of the angles of the shadows cast by a vertical stick at Syene (today known as Aswan) and another at Alexandria, at noon on 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 interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

This article makes the case that cost functions are the best available methodology for ensuring consistency between a state's educational accountability system and its education finance system. Because they are based on historical data and well-known statistical methods, cost functions are a particularly flexible and low-cost way to forecast what…

Predicting the future is a basic problem that people have to solve every day and a component of planning, decision making, memory, and causal reasoning. In this article, we present 5 experiments testing a Bayesian model of predicting the duration or extent of phenomena from their current state. This Bayesian model indicates how people should…

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

It is important to let students see the value of mathematics in design--and how mathematics lends perspective to problem solving. In this article, the author describes a water-service challenge which enables students to design a water utility system that uses surface runoff into an open reservoir as the potable water source. This challenge…

A directly applicable latent variable modeling procedure for classical item analysis is outlined. The method allows one to point and interval estimate item difficulty, item correlations, and item-total correlations for composites consisting of categorical items. The approach is readily employed in empirical research and as a by-product permits…

Imputation methods are popular for the handling of missing data in psychology. The methods generally consist of predicting missing data based on observed data, yielding a complete data set that is amiable to standard statistical analyses. In the context of Bayesian factor analysis, this article compares imputation under an unrestricted…

This article investigates the accuracy of examinee classification into performance categories and the estimation of the theta parameter for several item response theory (IRT) scaling techniques when applied to six administrations of a test. Previous research has investigated only two administrations; however, many testing programs equate tests…

Evaluation of the effectiveness of higher education has received unprecedented attention from stakeholders at many levels. The Voluntary System of Accountability (VSA) is one of the initiatives to evaluate institutional core educational outcomes (e.g., critical thinking, written communication) using standardized tests. As promising as the VSA…

This paper first discusses the relationship between Kullback-Leibler information (KL) and Fisher information in the context of multi-dimensional item response theory and is further interpreted for the two-dimensional case, from a geometric perspective. This explication should allow for a better understanding of the various item selection methods…