Despite its intuitive appeal and popularity, Thorndike's constant ratio (CR) model for unbiased selection is inherently inconsistent in "n"-free selection. Satisfaction of the condition for unbiased selection, when formulated in terms of success/acceptance probabilities, usually precludes satisfaction by the converse probabilities of…

This paper presents a new hierarchical classes model, called Tucker2-HICLAS, for binary three-way three-mode data. As any three-way hierarchical classes model, the Tucker2-HICLAS model includes a representation of the association relation among the three modes and a hierarchical classification of the elements of each mode. A distinctive feature of…

An in-depth investigation of the relationship between media effectiveness, essentiality, and amount of study was presented. Overall, effectiveness explains 48% of the variation in the amount of study. Students who found the media more effective studied the media more. Those media that were more effective were studied more. The relationship between…

Hierarchical Linear Models (HLM) have been used extensively for value-added analysis, adjusting for important student and school-level covariates such as socioeconomic status. A recently proposed alternative, the Layered Mixed Effects Model (LMEM) also analyzes learning gains, but ignores sociodemographic factors. Other features of LMEM, such as…

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Bridge to…

The present study examined the influence of family and classroom environments on the development of particular individual characteristics, including level of empathy, attitude to institutional authority and perceived social reputation, and the role these characteristics may in turn play in school aggression. Participants were 1319 adolescents aged…

Children live in a highly sophisticated world composed of interlocking complex systems. An appreciation and understanding of such systems is critical for making effective decisions about everyone's lives as individuals and as community members. This article addresses one approach to introducing children of all achievement levels to introductory…

When the character Yoda first appeared on the silver screen, his movements were due to the efforts of famed muppeteer Frank Oz. In "Star Wars Episode II: Attack of the Clones," Yoda returned to the movies but this time the character was not a puppet but a digital image within a computer. This paper discusses the role, or, more aptly, the force, of…

An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…

This paper, in a fashion easy to follow, illustrates the interesting relationship between structural equation modeling and canonical correlation analysis. Although computationally somewhat inconvenient, representing canonical correlation as a structural equation model may provide some information which is not available from conventional canonical…

N. S. Raju, W. J. van der Linden, and P. F. Fleer (in press) have proposed an item response theory-based, parametric procedure for the detection of differential item functioning (DIF)/differential test functioning (DTF) known as differential functioning of item and test (DFIT). DFIT can be used with dichotomous, polytomous, or multidimensional…

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…

Most researchers using factor analysis extract factors from a matrix of Pearson product-moment correlation coefficients. A method is presented for extracting factors in a non-parametric way, by extracting factors from a matrix of Spearman rho (rank correlation) coefficients. It is possible to factor analyze a matrix of association such that…