Developed are simple recursion formulas for generating the exact distribution of the longest run of heads, both for a fair coin and for a biased coin. Discusses the applications of runs-related phenomena such as molecular biology, Markov chains, geometric variables, and random variables. (YP)

The effect of large, within-examinee item difficulty variability on estimates of the proportion of consistent classification of examinees into mastery categories was studied over 2 test administrations for 100 simulated examinees. The proportion of consistent classifications was adequately estimated using the technique proposed by M. Subkoviak…

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

This article explores an application of combinations, geometric series, and elementary probability that arises in a Biblical setting. Describes examples of the applications such as the use of "urim and thummin." (YP)

An evolved form of the Edwards and Beckworth (1989) model for probability selection for Scholastic Achievement Test takers using truncated normal distributions is presented. It is shown that the arguments of Holland and Wainer are not sufficient to reject this model. (SLD)

Describes an introductory course on data, statistics, and probability given to first-year electronic engineering students at the University of Hull (United Kingdom); it is taught via workshops using spreadsheets. The four components are data and graphs, random data and statistics, probability distributions, and probability and events. (AEF)

Investigates the relationships between the parameters of the Simon-Yule model and the shapes of three bibliometric distributions: Lotka's Law of Scientific Productivity; Bradford's Law of Bibliometric Scattering; and Zipf's Law of Word Frequency. The results indicate that the probability of a new entry determines the characteristics of all three…

Presents a case study of a learner engaged with a probability paradox. The case illustrates a Connected Mathematics Project approach: that primary obstacles to learning probability are conceptual and epistemological and that engagement with paradox can be a powerful means of motivating learners to overcome these obstacles. (71 references)…

This paper encourages the use of multiple logistic analysis in early intervention research, to assess the degree of association of multiple factors (such as subject or situational characteristics) with a dichotomous outcome (such as benefitting or not benefitting from an intervention) and to estimate the probability of each outcome. (JDD)

The explicit, experimental introduction of a series of logical inconsistencies is described and recommended as a means of disrupting the faulty logic and, thereby, enhancing the use of more appropriate probabilistic reasoning by graduate students enrolled in an introductory inferential statistics course. (14 references) (JJK)

A model is proposed for the clinical synthesis of data from psychological tests of persons with visual impairments. The model integrates the concepts of the ideal type and Bayesian probability and compares actual test scores with ideal scores through use of a pattern similarity coefficient. A pilot study with Business Enterprise Program operators…

This tutorial summarizes some of the widely known limitations of tests of statistical significance and then focuses on extracting measures of variation accounted for as a supplement to significance testing. Two measures of variation accounted for, eta squared and omega squared, are discussed. Computational formulas, computational examples, and…

A theoretical model is proposed for confidence in knowledge based on the assumption that people are good judges of the reliability of their knowledge, provided that the knowledge is representatively sampled from a specified reference class as defined by E. Brunswik (1943). Experiments with 177 college students support the theory. (SLD)

A probabilistic choice model, based on L. L. Thurstone's Law of Comparative Judgment Case V, is developed for paired comparisons data about psychological stimuli. The model assumes that each stimulus is measured on a small number of physical variables. An algorithm for estimating parameters is illustrated with real data. (SLD)

Describes a theoretical model based on binary vectors that was developed to improve relevance in information retrieval systems. Earlier probabilistic models are examined, quadratic and linear discriminant functions are discussed, relationships between queries and documents are considered, and further research is suggested. (15 references) (LRW)