To determine if Rasch Model procedures have any utility for equating pre-existing tests, data from the equating phase of the Anchor Test Study (ATS) were reanalyzed. This management report summarizes the work completed in the project, describes the differences in this project and that of the ATS, and presents recommendations and conclusions to the…

Pearson's unrestricted chi-square procedure is reviewed, and an historical presentation of Neyman's restricted chi-square test is introduced with a discussion of its theory and applicability to education. An example of the Neyman procedure is discussed in detail to familiarize researchers with this useful technique for analyzing contingency…

Three topics in factor analysis are covered: a) a reliability coefficient for assessing the quality of a maximum likelihood factor analysis, b) an application of three-mode factor analysis to serial learning data, showing variations in learning curves over stages of learning and individuals, and c) the use of personal probability functions to…

Aitkin's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are scale free and asymptotically efficient. The estimates are computed by a rapidly…

The problem of comparing proportions when some data are missing is investigated, and determination is made of what statistical techniques are appropriate under each of several probability models describing the observations likely to be missing. Monte Carlo methods were used to investigate the properties of standard estimators under each of the…

A method for estimating power scores is described. By way of illustration, it is applied to 21 students who were improperly timed on a standard test. Some empirical results are given in support of the estimation procedure. (Author)

Two basic issues are discussed that involve the Carver model of the relationship between test score and knowledge. The first of these concerns different types of tests which have different probabilities of obtaining the correct answer due to guessing. A derivation is shown which places different test types "on-a-par"--meaning that two tests are…

Since the primary purpose of classical testing is to rank order examinees consistently, the absolute value of the true score has been relatively unimportant. However, the major purpose of criterion referenced testing is to estimate the true capabilities of examinees to perform specific tasks. Hence, the problems of true score determination assume…

The author presents an approach to the teaching of undergraduate introductory probability and statistics. He also presents experimental evidence that suggests the approach helps students rely upon probability theory in making estimates for the likelihood of events rather than rely upon heuristic principles which may bias probability estimates. (MN)

The principles of modern genetics are extended to study the extinction probabilities of such genetic diseases as sickle-cell anemia, Tay-Sachs disease, and cystic fibrosis. (JT)

After a review of the disadvantages of linear models for estimating the probability of academic success from previous school records and admission test results, the use of a probit model is proposed. The model is illustrated with admissions data from the Ecole des Hautes Etudes Commerciales in Montreal. (Author/BW)

The problems involved in making reservations for airline flights is discussed in creating a mathematical model designed to maximize an airline's income. One issue not considered in the model is any public relations problem the airline may have. The model does take into account the issue of denied boarding compensation. (MP)

The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)

Presents two case studies of learners attempting to understand the concept of normal distribution, specifically why physical phenomena such as height fall into normal distributions. Draws conclusions about a Connected Mathematics learning environment that enables confrontation with epistemological anxiety and the features of modeling languages…