Over the last decades, a multitude of results in educational and psychological research have shown that the implementation of multiple external representations (MERs) in educational contexts represents a valuable tool for fostering learning and problem-solving skills. The context of science, technology, engineering, and mathematics (STEM)…

Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and…

Conducting research with human subjects can be difficult because of limited sample sizes and small empirical effects. We demonstrate that this problem can yield patterns of results that are practically indistinguishable from flipping a coin to determine the direction of treatment effects. We use this idea of random conclusions to establish a…

Partial correlation coefficients are often used as effect sizes in the meta-analysis and systematic review of multiple regression analysis research results. There are two well-known formulas for the variance and thereby for the standard error (SE) of partial correlation coefficients (PCC). One is considered the "correct" variance in the…

Evidence of confusion in intermediate accounting textbooks regarding the annual percentage rate (APR) and annual effective rate (AER) is presented. The APR and AER are briefly discussed in the context of a note payable and correct formulas for computing each is provided. Representative examples of the types of confusion that we found is presented…

Huntington's disease (HD), an autosomal-dominant genetic disorder, has historically been viewed as a degenerative movement disorder but it also includes psychiatric symptoms and progressive cognitive decline. There has been a lack of consensus in the literature about whether or not cognitive signs can be detected in carriers before clinical…

Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.

Discusses the measurement of the growth and obsolescence of literature and shows that growth and obsolescence can be studied by the same mathematical techniques. A combined growth-obsolescence theory is presented that can be measured with continuous rates, and three earlier papers are reconsidered and results are reproven. (Contains 18…

Reviews informetric, or bibliometric, distributions, including Lotka's, rank frequency distributions, Zipf functions, Mandelbrot functions, Leimkuhler functions, and Bradford's formulations. An example of the use of these techniques to analyze song texts of Thomas Dolby is given, and results are reported that show a fit with a Leimkuhler function.…

Proposes that document space and query space have different structures in information retrieval and discusses similarity measures, term independence, and linear structure. Examples are given using the retrieval functions of dot-product, the cosine measure, the coefficient of Jaccard, and the overlap function. (Contains 28 references.) (LRW)

Discussion of probabilistic information retrieval systems highlights the probability ranking principle and discusses when the standard retrieval policy is optimal. Topics discussed include calibration and refinement; independent assessment of relevance by the inquirer; certainty about the computed probabilities of relevance; and confidence and…

Cohen's (TM 504 890) formal rules of intuitive probability lack normative or descriptive appeal, and his interpretation of the author's findings is not compelling. (CP)

Describes an empirical Bayes method for predicting future use of library materials. Data from the University of Saskatchewan are used to illustrate practical applications of the model for simple prediction, prediction profiles, and prediction intervals. (21 references) (MES)

Compares the performance of inverted and signature file organizations in handling incrementally specified Boolean queries to an information retrieval system. The discussion covers the impact of more sophisticated signature file organizations, related problems, and possible future work. (65 references) (CLB)

Learnability theory is an attempt to illuminate the concept of learnability using a mathematical model of learning. Two models of learning of categorial grammars are examined here: the standard model, in which sentences presented to the learner are flat strings of words, and one in which sentences are presented in the form of functor-argument…