This article addresses the problem of small nonprobability samples in research in the education of the deaf and hard of hearing in the face of a current and increasing emphasis on "scientifically based research" as required by recent No Child Left Behind (NCLB) federal legislation. The authors examine the gains and losses in information…

We describe a principled way of imposing a metric representing dissimilarities on any discrete set of stimuli (symbols, handwritings, consumer products, X-ray films, etc.), given the probabilities with which they are discriminated from each other by a perceiving system, such as an organism, person, group of experts, neuronal structure, technical…

This paper describes a study, now in progress, of new methods for representing the sampling variability of Mantel-Haenszel differential item functioning (DIF) results, based on the system for categorizing the severity of DIF that is now in place at the Educational Testing Service. The methods, which involve a Bayesian elaboration of procedures…

Based on a synthesis of the literature and observations of young children over 2 years, a framework for assessing probabilistic thinking was formulated, refined, and validated. For each of four major constructs incorporated into this framework--sample space, probability of an event, probability comparisons, and conditional probability--four…

A test of statistical significance is a procedure for determining how likely a result is assuming a null hypothesis to be true with randomization and a sample of size n (the given size in the study). Randomization, which refers to random sampling and random assignment, is important because it ensures the independence of observations, but it does…

Induced probabilities have been largely ignored by educational researchers. Simply stated, if a new or random variable is defined in terms of a first random variable, then induced probability is the probability or density of the new random variable that can be found by summation or integration over the appropriate domains of the original random…

Previous work on the effects of dimensionality on parameter estimation was extended from dichotomous models to the polytomous graded response (GR) model. A multidimensional GR model was developed to generate data in one-, two-, and three-dimensions, with two- and three-dimensional conditions varying in their interdimensional associations. Test…

The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for…

The logit methodology provides a unique way of examining input-output relationships for social systems where the principal output of the analysis is a probability of some action or state. (Author)

Concerns about students' difficulties in statistical reasoning led to a study which explored year 11 (14 to 16 year-olds) students' ideas in this area. The study focussed on sampling variability, probability, descriptive statistics and graphical representations. This paper presents and discusses the ways in which students made sense of sampling…

Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…

This publication is designed to aid schools in planning a course of study for students in Course III Mathematics in New York State schools. This guide continues the developmental program begun in Course I. It is intended to serve as the Regents syllabus for the third year of the academic sequence for a New York State Regents diploma. This document…

Expert systems can be used to aid decision making. A computerized adaptive test (CAT) is one kind of expert system, although it is not commonly recognized as such. A new approach, termed EXSPRT, was devised that combines expert systems reasoning and sequential probability ratio test stopping rules. EXSPRT-R uses random selection of test items,…

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

The Comprehensive School Mathematics Program (CSMP) is described as a complete elementary mathematics curriculum that provides a natural place for probability and statistics. The CSMP approach of innovative, pictorial techniques is summarized here, with emphasis on methods and activities seen as proven successful through the enthusiastic reception…