The standard approach to the general rules for differentiation is to first derive the power, product, and quotient rules and then derive the chain rule. In this short article we give an approach to these rules which uses the chain rule as the main tool in deriving the power, product, and quotient rules in a manner which is more student-friendly…

We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by…

We consider the estimation of probabilistic ranking models in the context of conjoint experiments. By using approximate rather than exact ranking probabilities, we avoided the computation of high-dimensional integrals. We extended the approximation technique proposed by Henery (1981) in the context of the Thurstone-Mosteller-Daniels model to any…

Multilevel modeling (MLM) is a popular way of assessing mediation effects with clustered data. Two important limitations of this approach have been identified in prior research and a theoretical rationale has been provided for why multilevel structural equation modeling (MSEM) should be preferred. However, to date, no empirical evidence of MSEM's…

This paper examines whether conclusions about the relationship between education and labor market risk depend on the use of commonly applied procedures to clean data of extreme values. The analysis uses fifteen years of data from the Panel Study of Income Dynamics to demonstrate that conclusions about the relationship between education and labor…

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…

This study discusses the justifiability of item parameter estimation in incomplete testing designs in item response theory. Marginal maximum likelihood (MML) as well as conditional maximum likelihood (CML) procedures are considered in three commonly used incomplete designs: random incomplete, multistage testing and targeted testing designs.…

Geologic time is a crucial component of any geoscientist's training. Essential knowledge of geologic time includes rates of geologic processes and the associated time it takes for geologic features to form, yet measuring conceptual thinking abilities in these domains is challenging. We describe development and initial application of the Landscape…

Purpose: Counting and exact arithmetic rely on language-based representations, whereas number comparison and approximate arithmetic involve approximate quantity-based representations that are available early in life, before the first stages of language acquisition. The objective of this study was to examine the impact of language abilities on the…

Achieving the United Nations Millennium Development Goals (MDGs) remains a major challenge, particularly in developing countries. Specifically, achieving the target of completing a full course of primary schooling among all children, which is goal two, is a major challenge for Sub-Saharan Africa. Though literature consensually suggests that the…

This paper re-considers the widespread use of value-added approaches to estimate school "effects", and shows the results to be very unstable over time. The paper uses as an example the contextualised value-added scores of all secondary schools in England. The study asks how many schools with at least 99% of their pupils included in the…

A homework assignment is outlined in which students learn Computational Fluid Dynamics (CFD) concepts of discretization, numerical stability and accuracy, and verification in a hands-on manner by solving physically realistic problems of practical interest to engineers. The students solve a transient-diffusion problem numerically using the common…

One option for Extension professionals wishing to use free statistical software is to use online calculators, which are useful for common, simple analyses. A second option is to use a free computing environment capable of performing statistical analyses, like R-project. R-project is free, cross-platform, powerful, and respected, but may be…

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a "black box" to the students. Thus, although correct models are…

This article outlines a discussion had by a group of prospective teachers regarding questions that remained after their previous experiences as students. The discussion was focused on the rules associated with the division of decimals. Prospective teachers' initial discussion showed a strong tendency to handle the rules as taken-for-granted…