This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments such as might occur in educational research. Three applications illustrate the approach. (SLD)

A Bayesian approach to the testing of competing covariance structures is developed. Approximate posterior probabilities are easily obtained from the chi square values and other known constants. The approach is illustrated using an example that demonstrates how the prior probabilities can alter results concerning the preferred model specification.…

Minkowski distances are used to indicate similarity of two vectors in an N-dimensional space. How to compute the probability function, the expectation, and the variance for Minkowski distances and the special cases City-block distance and Euclidean distance. Critical values for tests of significance are presented in tables. (SLD)

Applies elementary concepts of probability to a hotly debated question in football. Shows that the probability of winning is the same either way but the probability of losing is greater under the one-first strategy. (MKR)

Surveys of (n=200 in 5 schools) secondary school students' preconceptions of probability found that, although these students had had no formal instruction in probability, they did have some notion of the topic. Includes survey. (Author/MKR)

This paper demonstrates that two major tests for two-by-two tables, Fisher's exact and Pearson's chi-square tests, are highly related from a Bayesian perspective. A formal similarity is demonstrated in small samples, and reasons for the relationship are discussed. (SLD)

A stochastic judgment model (SJM) is presented as a framework for addressing issues in statement verification and probability judgment. Results of 5 experiments with 264 undergraduates support the validity of the model and provide new information that is interpreted in terms of the SJM. (SLD)

Suggests a probabilistic method to compute the term relationships from relevance information, which complements the studies on a nonprobabilistic technique called pseudo-classification. A quadratic ranking function is derived by incorporating the term-by-term relationships. Procedures for estimating the required parameters are provided by…

Analysis of data from 2,542 respondents in the 1988 Displaced Workers Survey assessed the effects of written advance notice of plant closings on reemployment and earnings. Results suggest that notification was effective in reducing earnings losses and the probability of unemployment only when received two months before the plant closing. (SK)

Presents a mathematics problem on probability and matrices placed in a context with insects. Provides an overview, prerequisites, materials needed, and worksheets. (ASK)

Presents several classroom demonstrations, based on well-known statistical ideas, that have sparked student involvement in introductory undergraduate courses in probability and statistics. Contains descriptions of 10 demonstrations. (SLD)

Discusses an old and quite surprising musical example that provides good challenges in probability theory ranging from practical routine computations to fundamental and philosophical ones, and extended with the engineering design task of generating random numbers. (ASK)

Points out the high percentage of African-American boys that believe that they can make a living playing professional sports and presents an activity that addresses the probability of a student athlete becoming a professional athlete. (YDS)

Reports on a study in which anchoring probability situations that are conceptually analogous to misconception-prone target probability situations were generated and tested with secondary mathematics students. Reports that a follow up test showed that 65% of the reconstructed knowledge was retained after six months. (Author/MM)

Tackles a tricky problem of probability based on the well-known carnival game Chuck-a-Luck which, at first glance, appears to favor the bettor. Presents an activity in which students correct a common fallacy in probabilistic reasoning and extend play to a gambler's ruin analysis. (Author/ASK)