Probability is more increasingly recognized as a priority in elementary school. In this article, the author argues that if students have a strong understanding of experimental probability, notions of theoretical probability will be easier for the student to understand. In particular, students need extensive experience with experiments using…

A rationale is proposed for approximating the normal distribution with a logistic distribution using a scaling constant based on minimizing the Kullback-Leibler (KL) information, that is, the expected amount of information available in a sample to distinguish between two competing distributions using a likelihood ratio (LR) test, assuming one of…

This article concludes the serialization of the Royal Statistical Society's Schools Lecture for 2004, on "Lies and statistics".

This article introduces 2 new sources of bias in probability judgment, discrimination failure and inhibition failure, which are conceptualized as arising from an interaction between error prone memory processes and a support theory like comparison process. Both sources of bias stem from the influence of irrelevant information on participants'…

A simple, direct condition is formulated for determining the mode(s) of a probability mass function. This condition is then applied to the Poisson and hypergeometric mass functions.

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

Three experiments compared the learning of lower-dimensional family resemblance categories (4 dimensions) with the learning of higher-dimensional ones (8 dimensions). Category-learning models incorporating error-driven learning, hypothesis testing, or limited capacity attention predict that additional dimensions should either increase learning…

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

The experiments reported in this article used a delayed same/different sentence matching task with concurrent measurement of eye movements to investigate the nature of the plausibility effect. The results clearly show that plausibility effects are not due to low level lexical associative processes, but arise as a consequence of the processing of…

Although previous research has not consistently shown that uncertainty about academic major negatively impacts graduation, commitment is largely believed to affect college students' success. We investigated the impact of institutional commitment, commitment to an educational goal, and commitment to an academic major on the probabilities of…

This booklet suggests activities that reflect findings from recent educational research on curriculum, assessment, and instruction, as well as the National Council of Teachers of Mathematics Standards pertaining to probability and statistics. Each teacher's guide for the 13 hands-on activities includes objectives stemming from NCTM…

The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

Considered in this paper are a mathematical discussion and an algorithm, and a computer program for Fisher's test. (Author)

ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…

Examines the question of how large a sample must be in order to produce empirical Bayes estimates which are preferable to other commonly used estimates, such as proportion correct observed score. (Author/RC)