In the context of a department of applied mathematics, a program assessment was conducted to assess the departmental goal of enabling undergraduate students to recognize, appreciate, and apply the power of computational tools in solving mathematical problems that cannot be solved by hand, or would require extensive and tedious hand computation. A…

(Purpose) The purpose of this paper is to present an easy-to-understand primer on three important concepts of factor analysis: Factor scores, structure coefficients, and communality coefficients. Given that statistical analyses are a part of a global general linear model (GLM), and utilize weights as an integral part of analyses (Thompson, 2006;…

The Burr families (Type III and Type XII) of distributions are traditionally used in the context of statistical modeling and for simulating non-normal distributions with moment-based parameters (e.g., Skew and Kurtosis). In educational and psychological studies, the Burr families of distributions can be used to simulate extremely asymmetrical and…

The Isoperimetric Quotient, or IQ, introduced by G. Polya, characterizes the degree of sphericity of a convex solid. This paper obtains closed form expressions for the surface area and volume of any Archimedean polyhedron in terms of the integers specifying the type and number of regular polygons occurring around each vertex. Similar results are…

Bioelectrical impedance analysis (BIA) is a widely used method for estimating body composition, yet issues concerning its validity persist in the literature. The purpose of this study was to validate percentage of body fat (BF) values estimated from BIA and skinfold (SF) with those obtained from hydrodensitometry (HD). Percent BF values measured…

In this article we explore the consequences of modifying the common definition of a parabola by considering the locus of all points equidistant from a focus and (not necessarily linear) directrix. The resulting derived curves, which we call "generalized parabolas," are often quite beautiful and possess many interesting properties. We show that…

Subitizing is the immediate apprehension of the exact number of items in small sets. Despite more than a 100 years of research around this phenomenon, its nature and origin are still unknown. One view posits that it reflects a number estimation process common for small and large sets, which precision decreases as the number of items increases,…

In the first part of the paper, using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ([mu]). A parametric equation for the trajectory of the particle is also obtained. In the second part of the paper, the motion of a sphere on the inclined plane is…

Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the…

Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

How effective is training frogs to jump? This is perhaps the most frequent question in biology that is subjected to statistical analysis: does a treatment make a difference? One can examine whether there is indeed a training effect, by first assuming the opposite. That is, the authors assume that training has no effect on the mean distance jumped.…

This article comes from a question asked by a student of mine: if the Sun radiates energy in the form of electromagnetic waves, could they shift the Earth from its current orbit on a suitable timescale? The answer to such a question is apparently obvious and trivial. Nevertheless, it requires an instructive reasoning and interesting estimates of…

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Purpose: To estimate false-positive rates for rules proposed to identify early noise-induced hearing loss (NIHL) using the presence of notches in audiograms. Method: Audiograms collected from school-age children in a national survey of health and nutrition (the Third National Health and Nutrition Examination Survey [NHANES III]; National Center…