A simple experiment is described to compare the descent time between two vertically separated points when an object slides down tracks of varying shape. A surprising result is that the descent time is shortest when it follows a circular track rather than a cycloidal track. Cycloidal tracks are usually predicted to result in the shortest descent…

Currently the design standards for single case experimental designs (SCEDs) are based on validity considerations as prescribed by the What Works Clearinghouse. However, there is a need for design considerations such as power based on statistical analyses. We compute and derive power using computations for (AB)[superscript k] designs with multiple…

Background/Context: Attrition has been described as "the Achilles Heel of the randomized experiment" (Shadish et al., 1998 p.3). Attrition looms as a threat because it can undermine group equivalence, eroding the methodological strength at the heart of a randomized evaluation. In particular, attrition could result in unobserved…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…

Once research questions are posed, researchers must answer many a priori questions regarding research design before analysis can be performed and any conclusions can be made, including sample selection criteria, data collection method, model specification, analysis and estimation technique. The choices made by researchers along this forking path…

The purpose of the study is to systematically review studies investigating the script fading procedure on individuals with autism and also determine the quality of the studies and the effect size related to the calculations of the percentage of nonoverlapping data (PND) and the percentage of data exceeding the median (PEM) in the studies. The…

Traditional physical chemistry conceptions of reaction mechanism are formulated in terms of stationary points of an Arrhenius-style "energy profile" that differs sharply (in purpose and form) from the corresponding Robinson-style "arrow-pushing" mechanistic conceptions of organic chemistry. We show here how these diverse…

In this article, we present a two-stage estimation approach applied to multilevel latent class analysis (LCA) with covariates. We separate the estimation of the measurement and structural model. This makes the extension of the structural model computationally efficient. We investigate the robustness against misspecifications of the proposed…

In this paper, we share the results of the piloting of national diagnostic assessments for strategic calculation with Grade 3 learners in South Africa. The diagnostic assessment pilot intervention was focused on promoting strategic use of calculation strategies and aimed to move learners on from the concrete one-to-one counting methods that…

In the era of the "reproducibility crisis" and the "P-value controversy" new ways of presentation and interpretation of the results of a meta-analysis are desirable. One suggestion that has been made for single studies almost six decades ago and taken up now and then is the P-value function. For a given outcome, this function…

The purpose of this research note is to introduce a latent growth curve reconstruction approach based on the Tabu search algorithm. The approach algorithmically enables researchers to optimally determine at both the individual and the group levels the order of the polynomial needed to represent the latent growth curve model. The procedure is…

The acid-catalyzed dehydration of regioisomeric methylcyclohexanols is a classic organic chemistry experiment featured in a variety of laboratory textbooks and literature. The mechanistic details of this reaction have received an inconsistent and occasionally inaccurate treatment, wherein the reaction has been described as a mix of E1, E2-like,…

Gaussian-2-Blender is an open-source application programming interface (API) written in Python that allows for the conversion of Gaussian input files to 3D objects of different formats. This new tool was developed in response to the shortcomings of available programs to import Gaussian calculations into augmented reality (AR) or virtual reality…

Inconsistent filtering of force plate data persists in published studies. Previous evidence suggests that low pass filtering produces the largest error when calculating jump height, but used jump height from unfiltered force plate data as the criterion. This study investigated the effects of low pass filtering on jump height calculated from force…

We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the previous results to determine the quadratic factors of polynomials over commutative coefficient rings and, in particular, to completely factorize in Z[x] any…