In this article, the authors describe how a Java applet can help to build learners' intuitions about basic ideas of algebra. "Matchbox Algebra" is a Java applet the authors have designed to enable learners to grasp a key idea in learning algebra: that the letter "x" may be thought of as representing an as-yet-unknown number. They describe the…

A special but common type of scenario is one in which a company has a promotion that is designed to make the customer purchase more of their product than they otherwise might. Although this can be aimed specifically at children, it really applies to all persons. The basic premise is that the company issues a "set" of different items or…

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…

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…

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 partial credit model (PCM) (G. N. Masters, 1982) can be viewed as a generalization of the Rasch model for dichotomous items to the case of polytomous items. In many cases, the PCM is too restrictive to fit the data. Several generalizations of the PCM have been proposed. In this paper, a generalization of the PCM (GPCM), a further…

This discussion of new methods for calibrating item response theory (IRT) models looks into new optimization procedures, such as the Genetic Algorithm (GA) to improve on the use of the Newton-Raphson procedure. The advantages of using a global optimization procedure like GA is that this kind of procedure is not easily affected by local optima and…

In the technique developed by K. G. Joreskog to solve the problem for oblique rotation to a specified simple structure, the basic concept is that the simple structure solution itself is determined only by the zero coefficients of the reference-structure matrix and not by the coefficients of non-zero magnitude. Following this, prior information…

Cross-validation, an economical method for assessing whether sample results will generalize, is discussed in this paper. Cross-validation is an invariance technique that uses two subsets of the data sample to derive discriminant function coefficients. The two sets of coefficients are then used with each data subset to derive discriminant function…

Conditional observed score (COS) and latent trait (LT) definitions of differential item functioning (DIF) are explored to determine when they are equivalent. COS methods rely solely on observed measurements, and LT methods model the response to an item as a function of an unobserved hypothetical latent ability or trait. For the case of dichotomous…

Previous methods for estimating the conditional standard error of measurement (CSEM) at specific score or ability levels are critically discussed, and a brief summary of prior empirical results is given. A new method is developed which avoids theoretical problems inherent in some prior methods, is easy to implement, and estimates not only a…

Trait psychology, psycho-dynamics, situationism, and interactionism, the four basic models of personality, are summarized; controversies they have generated and relevant research are discussed. Special emphasis is placed on interactional psychology as a model of personality theory and research. Controversial issues of personality such as…

The kappamax reliability index of domain-referenced tests is defined as the upper bound of kappa when all possibile cutoff scores are considered. Computational procedures for kappamax are described, as well as its approximation for long tests, based on Kuder-Richardson formula 21. The sampling error of kappamax, and the effects of test length and…

FANTAB is a computer program written in Fortran IV which helps design factorial analysis of variance tables and provides formulae for table entries. It is a computerization of a paper entitled: "Rules of Thumb for Writing the Anova Table" (Millman and Glass, 1967). FANTAB is appropriate for factorial models which have two, three, or four…