Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors…

While infants' ability to discriminate quantities has been extensively studied, showing that this competence is present even in neonates, the ability to compute ordinal relations between magnitudes has received much less attention. Here we show that the ability to represent ordinal information embedded in size-based sequences is apparent at 4…

Most biological scientists conduct experiments to look for effects, and test the results statistically. One of the commonly used test is Student's t test. However, this test concentrates on a very limited question. The authors assume that there is no effect in the experiment, and then estimate the possibility that they could have obtained these…

This article has 3 objectives that build on each other. First, we demonstrate how to obtain maximum likelihood estimates for dynamic factor models (the direct autoregressive factor score model) with arbitrary "T" and "N" by means of structural equation modeling (SEM) and compare the approach to existing methods. Second, we go beyond standard time…

Physics instruction looks different from one classroom to the next; however, the outcome of those classrooms should be one and the same. Students should understand simple concepts and be able to transfer concepts to more complex problems. In this lesson, I would like to show you how I provide students an opportunity to explore their ideas before…

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…

Since the founding of the Nation, science, technology, engineering, and mathematics (STEM) have been a source of inspirational discoveries and transformative technological advances, helping the United States develop the world's most competitive economy and preserving peace through strength. The pace of innovation is accelerating globally, and with…

We report a randomised controlled trial evaluation of an intensive one-to-one numeracy programme--"Numbers Count"--which formed part of the previous government's numeracy policy intervention--"Every Child Counts." We rigorously designed and conducted the trial to CONSORT guidelines. We used a pragmatic waiting list design to…

Several factors could cause variability in item response theory (IRT) linking and equating procedures, such as the variability across examinee samples and/or test items, seasonality, regional differences, native language diversity, gender, and other demographic variables. Hence, the following question arises: Is it possible to select optimal…

The transition from study to work is an important one. The jobs that graduates secure after completing their studies may very well shape the trajectory of their future careers, so an understanding of how job search influences employment outcomes has significant implications for theory and higher education practice. This article specifically…

The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…

Researchers have proposed that an explicit reasoning system is responsible for learning rule-based category structures and that a separate implicit, procedural-learning system is responsible for learning information-integration category structures. As evidence for this multiple-system hypothesis, researchers report a dissociation based on…

Osborne and Waters (2002) focused on checking some of the assumptions of multiple linear regression. In a critique of that paper, Williams, Grajales, and Kurkiewicz correctly clarify that regression models estimated using ordinary least squares require the assumption of normally distributed errors, but not the assumption of normally distributed…

Students' success in solving problems involving proportional reasoning is an indication that they have moved beyond additive thinking to multiplicative thinking. However, classroom work indicates that many students do not reason proportionally in many practical contexts. The authors discuss a particular task that reveals students'…

A project for students in an upper-level course in quantum or computational chemistry is described in which they are introduced to the concepts and applications of a high quality, ab initio treatment of the ground-state potential energy curve (PEC) for H[subscript 2] and D[subscript 2]. Using a commercial computational chemistry application and a…