Describes an activity in which students investigate patterns and discrete mathematics found in telephone numbers. (YDS)

An Edgeworth approximation for accurate significance probabilities for the Wilcoxon two-sample test is substantially simplified. A method is developed that allows quick calculations of very accurate probabilities. Exact formulas are given for most of the remaining cases, and tables are presented comparing the new simplification to likely…

Presents a probability model of the occurrence of index terms used to derive discrete distributions which are mixtures of Poisson and negative binomial distributions. These distributions give better fits than the simpler Zipf distribution, have the advantage of being more explanatory, and can incorporate a time parameter if necessary. (25…

Demonstrates the use of the Waring distribution as a model for the frequency distribution of scientific productivity. Methods for testing the fit at both ends of the distribution, as well as for estimating the parameters of the distribution and the total number of scientists, are outlined. (16 references) (Author/CLB)

It is shown that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Analysis of several thousand solutions to Bayesian problems showed that when information was presented in frequency formats, statistically naive participants derived up to 50% of inferences by Bayesian…

Probability terms were scaled by 3 methods as a result of a survey of undergraduate students (n=194): rank order, percentage estimate, and successive interval. Discusses implications for the selection and placement of probability terms on rating scales in the development of assessment instruments. (JPS)

Discusses models for the distribution of words in text and proposes a new model based on clustering that can be used to estimate the probability that a document contains a particular word as well as the number of distinct words in a document. Zipf's law and the Poisson approximation are also discussed. (18 references) (LRW)

A systematic investigation of the Grice modeling scheme for response time (RT) clarifies fundamental notions about RT modeling. The analysis presented can be used to determine what in a certain RT model constitutes a set of empirically testable assumptions and what is merely an arbitrary choice of mathematical language. (SLD)

Discussion of sampling methods used in information science research focuses on Fussler's method for sampling catalog cards and on sampling by length. Highlights include simple random sampling, sampling with probability equal to size without replacement, sampling with replacement, and examples of estimating the number of books on shelves in certain…

Introduces and discusses the rationale and procedures of two nonparametric approaches to estimating the operating characteristic of a discrete item response, or the conditional probability, given the latent trait, that the examinee's response be that specific response. (SLD)

Presents a game designed as a chance-and-data activity that can be used to illustrate the use of probability-tree diagrams and multiplication and addition rules of probability. (ASK)

Attempts to show how genes and environments cooperate in the construction of organisms, focusing on how genes require environmental and behavioral inputs to function appropriately during the normal course of human development. The discussion is related to a model of probabilistic epigenesis. (SLD)

Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)

Examined how 6- to 9-year-olds and adults judged expected value of complex gambles in which alternative outcomes had different prizes. Found that participants at all ages used multiplication rule for integrating probability and value of each individual outcome, and based judgment of overall expected value on alternative outcomes. Even youngest…

Two versions of the Smoking Consequences Questionnaire for adults were developed and tested with 407 smokers and nonsmokers. The version with probability items appeared to have greater construct validity than the version with subjective expected utility items. The scale reflects the refinement of smokers' outcome expectancies with experience. (SLD)