Empirical Bayes point estimates of true score may be obtained if the distribution of observed score for a fixed examinee is approximated in one of several ways by a well-known compound binomial model. The Bayes estimates of true score may be expressed in terms of the observed score distribution and the distribution of a hypothetical binomial test.…

The educational system is characterized by a vector matrix differential equation, and it is shown that the concepts of modern control theory such as observability, controllability, and optimal control can give deeper insight into the behavior of the educational system. The identification of the system dynamics and the definition of a realistic…

This report describes the results of preliminary work by the Human Resources Research Organization to develop a comprehensive theory for structuring subject matter. The report focuses on the first three of five components that any comprehensive model of instruction should include: (1) a representation of the subject matter to be taught; (2) a…

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

A new approach to deriving human performance measures and criteria for use in automatically evaluating trainee performance is described. Ultimately, this approach will allow automatic measurement of pilot performance in a flight simulator or from recorded in-flight data. An efficient method of representing performance data within a computer is…

A simple normative theory applicable to public library services was developed as a tool to aid libraries in answering the question: which books should be bought by the library? Although developed for normative purposes, the theory generates testable predictions. It is relevant to measuring benefits from services which are provided publicly because…

The research on covariance structure analysis is reviewed, and various restrictions on the parameter matrices of the general model are delineated. Models employing two particular restrictions (where the matrix of weights is completely specified and is either scaled--by some unknown but estimable matrix of scaling weights--or unscaled) are…

This paper describes three models of learning theories, derives optimal presentation strategies for the models, and compares the effectiveness of the strategies in two computer assisted instruction experiments. The three models described are: 1) the linear, or response-insensitive model, in which the error probability for a given item depends on…

This study develops an input-output model for making employment projections and applies it to the Oregon economy. Using published data and guided estimates, the study provides an approximation of the structure of the Oregon economy in 1963, as the first step in the systematic investigation of the State's economic and trade transactions. This…

Presented are the results of a study conducted to develop algorithms for ordering and organizing data that can be presented in a two-dimensional matrix form. The purpose of the work was to develop methods to extract latent data patterns, grouping, and structural relationships which are not apparent from the raw matrix data. The algorithms…

This collection of 17 articles concerning the application of mathematical models and techniques to the study of literary style is an attempt to overcome the communication barriers that exist between scholars in the various fields that find their meeting ground in statistical stylistics. The articles selected were chosen to represent the best…

The author suggests that mathematical formulas could provide some direct and easily understandable frameworks for analogies in literary criticism. Most studies of textual problems, he points out, either have failed to use full mathematical models or have been reckless with the inherent limits of these techniques. Enumeration of linguistic traits…

This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms,…

An equation was derived to determine the relationship between the pooled within-subgroup r (correlation coefficient) and the r obtained from the total group data. It was, thus, possible to assess the amount of distortion introduced by pooling heterogeneous subgroups. As a basis for deciding whether to pool two subgroups in order to calculate a…

Rooted binary trees with weighted nodes are structures encountered in many areas, such as coding theory, searching and sorting, information storage and retrieval. The path length is a meaningful quantity which gives indications about the expected time of a search or the length of a code, for example. In this paper, two sharp bounds for the total…