Three separate papers are included in this report. The first describes a two-stage procedure for choosing from among several instructional programs the one which maximizes the probability of passing the test. The second gives the exact sample sizes required to determine whether a squared multiple correlation coefficient is above or below a known…

Three equating methods were compared in terms of magnitude of scale drift: equipercentile equating, linear equating, and item response theory (IRT) equating. A sample of approximately 2670 cases was selected for each pairing of a form of the Scholastic Aptitude Tests (SAT) and an anchor test. Of the two conventional equating methods,…

Conducted to design software partitioning techniques for use by the Air Force to partition a large flight simulator program for optimal execution on alternative configurations, this study resulted in a mathematical model which defines characteristics for an optimal partition, and a manually demonstrated partitioning algorithm design which…

Present systems for the apportionment of grants from the state or federal level to local public school districts are based primarily on measures of district wealth as modified by weightings for the characteristics of the student population. Until recently little attention has been given to differences among districts in the costs of providing…

Whenever one uses ordinary least squares regression, one is making an implicit assumption that all of the independent variables have been measured without error. Such an assumption is obviously unrealistic for most social data. One approach for estimating such regression models is to measure implied coefficients between latent variables for which…

Internal validity is described as a matter of how well a particular instance of data collection or generation can be described and explained. It is a property of the procedures used in the collection or generation of data. The notion of internal validity is examined in order to establish a method of quantitatively estimating it. A coefficient of…

The advantages of the Delphi Technique are that it relies on collective expert judgment, prevents the excessive influence in decision-making of those in positions of status, and encourages consensus. The technique consists of five steps: (1) asking experts to list items relevant to a topic; (2) returning the list to the participants and asking…

The Goodman technique of log linear analysis is ideal for family research, because it is designed for categorical (non-quantitative) variables. Variables are dichotomized (for example, married/divorced, childless/with children) or otherwise categorized (for example, level of permissiveness, life cycle stage). Contingency tables are then…

A live tailored testing study was conducted to compare the results of using either the one-parameter logistic model or the three-parameter logistic model to measure the performance of college students on multiple choice vocabulary items. The results of the study showed the three-parameter tailored testing procedure to be superior to the…

Using data collected in a beginning teacher evaluation study, this paper attempts to show that time is an important input in producing learning. First the paper discusses equalization of tax bases in school districts, inequality in the distribution of inputs, and the importance of multiple outputs in schools. Next it describes an economic model of…

RESULTS OF FIFTY DIFFERENT RETRIEVAL METHODS AS APPLIED IN THREE EXPERIMENTAL RETRIEVAL SYSTEMS WERE SUBJECTED TO AN ANALYSIS SUGGESTED BY STATISTICAL DECISION THEORY. THE ANALYSIS USES A PREVIOUSLY-PROPOSED MEASURE OF EFFECTIVENESS AND DEMONSTRATES ITS SEVERAL PROPERTIES. SOME OF THESE PROPERTIES ARE--(1) IT ENABLES THE RETRIEVAL SYSTEM TO…

A MATHEMATICAL MODEL IS DEVELOPED TO STUDY THE PRODUCTION OF DOCTORAL, MASTER'S, AND BACHELOR'S DEGREES AND THEIR FEEDBACK INTO HIGHER EDUCATION. FEEDBACK IS DETERMINED BY A SET OF "BASIC BALANCE EQUATIONS" WHICH STATE THAT THE TOTAL RATE OF FLOW INTO A CATEGORY LESS THE RATE OF OUTFLOW IS EQUAL TO THE RATE OF ACCUMULATION OR GROWTH IN A GIVEN…

A MATHEMATICAL MODEL OF ESTABLISHED AND INDUSTRIALLY VALIDATED LEARNING AND FORGETTING THEORIES IS OUTLINED, AND A COMPUTER-EXECUTED HEURISTIC ALGORITHM FOR SELECTING THE BEST SCHEDULE FOR SUBJECT PRESENTATION IS GIVEN. FUNDAMENTAL PARAMETERS OF THE MODEL INCLUDE EDUCATION POTENTIAL, TYPE OF SUBJECT MATTER, TYPE OF LEARNER, TEACHING METHODS, AND…

This paper presents two extensions of the full-rank multivariate linear model that are particularly useful in multivariate analysis of covariance (MANCOVA) and repeated measurements designs. After a review of the basic full-rank model, an extension is described which allows restrictions of a more general nature. This model is useful in the…

Three approaches to the graphic representation of similarity and dissimilarity matrices are compared and contrasted. Specifically, Kruskal's multidimensional scaling, Johnson's hierarchical clustering, and Waern's graphing techniques are employed to depict, in two dimensions, data representing the structure of a set of botanical concepts. Each of…