Factor analysis models with ordinal indicators are often estimated using a 3-stage procedure where the last stage involves obtaining parameter estimates by least squares from the sample polychoric correlations. A simulation study involving 324 conditions (1,000 replications per condition) was performed to compare the performance of diagonally…

In this article, an integrated Bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item…

A simple spreadsheet program is presented that can be used by undergraduate students to calculate the lattice-site distributions in solids. A major strength of the method is the natural way in which the correct number of ions or atoms are present, or absent, at specific lattice distances. The expanding-cube method utilized is straightforward to…

Inducing causal relationships from observations is a classic problem in scientific inference, statistics, and machine learning. It is also a central part of human learning, and a task that people perform remarkably well given its notorious difficulties. People can learn causal structure in various settings, from diverse forms of data: observations…

The authors investigated the effectiveness of using high-preference (high-p) mathematics tasks for increasing task initiation of low-preference (low-p) mathematics tasks with a 13-year-old middle school student with autism. They used an ABAB design to determine the effectiveness of high-p tasks with to comply with low-p tasks. Results indicated…

The logarithmic transformation is often used in regression analysis for a variety of purposes such as the linearization of a nonlinear relationship between two or more variables. We have noticed that when this transformation is applied to the response variable, the computation of the point estimate of the conditional mean of the original response…

The bicycle provides a context-rich problem accessible to students in a first-year physics course, encircling several core physics principles such as conservation of total energy and angular momentum, dissipative forces, and vectors. In this article, I develop a simple numerical model that can be used by any first-year physics student to…

A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure…

In this work, we investigated first-year university students' skills in using the limit concept. They were expected to understand the relationship between the limit-value of a function at a point and the values of the function at nearby points. To this end, first-year students of a Turkish university were given two tests. The results showed that…

Various analyses have used the transfer rate as a performance indicator for community colleges, but the question of what constitutes an appropriate denominator in the transfer-rate equation remains a point of contention. This article examines the potential drawbacks of using student-reported educational goals to determine which students are…

The flight trajectory of a water rocket can be reasonably calculated if the magnitude of the drag coefficient is known. The experimental determination of this coefficient with enough precision is usually quite difficult, but in this paper we propose a simple free-fall experiment for undergraduate students to reasonably estimate the drag…

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…

Traditional estimators of fit measures based on the noncentral chi-square distribution (root mean square error of approximation [RMSEA], Steiger's [gamma], etc.) tend to overreject acceptable models when the sample size is small. To handle this problem, it is proposed to employ Bartlett's (1950), Yuan's (2005), or Swain's (1975) correction of the…

In this experiment, physical science students measured the mass of several soda cans, measured the mass and volume of water displaced when these cans were placed in water, and determined whether these cans sank or floated in water. Then, the students plotted graphs of the mass of displaced water versus the volume of displaced water, the mass of…

Morris water maze data are most commonly analyzed using repeated measures analysis of variance in which daily test sessions are analyzed as an unordered categorical variable. This approach, however, may lack power, relies heavily on post hoc tests of daily performance that can complicate interpretation, and does not target the nonlinear trends…