An attempt to build a mathematical model of a device that could learn geometry is discussed. The report discusses the background and motivation of the study, the coding problem, the derivation of Suppes "Stimulus-Response Theory of Finite Automata" used in the work in learning theory, and a summary of the technical work. (DB)

Omitted items cannot properly be treated as wrong when estimating ability and item parameters. A convenient method for utilizing the information provided by omissions is presented. Some theoretical and considerable empirical justification is adduced for the estimates obtained by both old and new methods. (Author)

This report, a technical appendix to The Performance Contracting Concept in Education (EA 003 602), summarizes the mathematical models that have been developed to analyze contractual relationships and incentives. The report will be of interest primarily to theoreticians and analysts rather than educational administrators. (Author)

The behavior of focus samples central to the multiple-look model of Trabasso and Bower is examined by three methods. First, exact probabilities of success conditional upon a certain brief history of stimulation are determined. Second, possible states of the organism during the experiment are defined and a transition matrix for those states…

Proceeding from a unifying framework, the paper reviews recent developments in lexicographic orders, preferences, utilities, probabilities and decision rules. Several new results are included. (see also: LI 004 160) (Author)

Statistical inference concerning the parameters of k multivariate normal populations is considered. Several models in which the parameters have certain hierarchical relationships are discussed, in particular as related to testing the hypothesis that k psychological tests are parallel forms of the same test. The report contains the following…

A model for multiple choice test-taking behavior is proposed which is different from those presently used for item sampling theory. A new theory is developed, which includes a new concept to facilitate comprehension of item sampling theory, a "number-known" score distribution. A major advantage of the model is that it accommodates data from…

In many circumstances it is appropriate to use the school as the unit of analysis. The variables measured on students must be aggregated to form a mean for each school. However, the means derived from the students sampled in a school will tend to fluctuate around the true mean for the school in a way determined by the within-school correlations…

A reanalysis of Shaycroft's matrix of intercorrelations of 10 test variables plus 4 random variables is discussed. Three different procedures were used in the reanalysis: (1) Image Component Analysis, (2) Uniqueness Rescaling Factor Analysis, and (3) Alpha Factor Analysis. The results of these analyses are presented in tables. It is concluded from…

CERTAIN SPECIFIC ASPECTS OF HYPOTHESIS TESTS USED FOR ANALYSIS OF RESULTS IN RANDOMIZED EXPERIMENTS WERE STUDIED--(1) THE DEVELOPMENT OF THE THEORETICAL FACTOR, THAT OF PROVIDING INFORMATION ON STATISTICAL TESTS FOR CERTAIN EXPERIMENTAL DESIGNS AND (2) THE DEVELOPMENT OF THE APPLIED ELEMENT, THAT OF SUPPLYING THE EXPERIMENTER WITH MACHINERY FOR…

A test bias definition, applicable at the item-level of a test is presented. The definition conceptually equates test bias with measuring different things in different groups, and operationally equates test bias with a difference in item fit to the Rasch Model, greater than one, between groups. It is suggested that the proposed definition avoids…

This paper considers estimation of parameters for a model currently being used to study the Illinois Interlibrary Loan Network (ILLINET) and presents a method for determining how much data should be collected and how it should be aggregated. Four classes of model parameters discussed: demands, probabilities of success, processing times, and…

Simulation models predicting resource requirements in higher education are compared (two developed in North American with two from Europe). They reveal a similar logic of relating student teaching loads to college and university resource requirements, but differences of educational program needs produce differing emphases. (JT)

Results of empirical comparisons of an inferential model of order analysis with factor analytic models were reported for two sets of data. On the prestructured data set both order and factor analytic models returned its dimensions of length, width and height, but on the random data set the factor analytic models indicated the presence of…

Proposes a new conceptual basis for visualizing the organization of information, or knowledge, which differentiates between the concept "vectors" for a field of knowledge represented in a multidimensional space, and the state "vectors" for a person based on his understanding of these concepts, and the representational…