Two optimalization models for the construction of tests with a maximal value of coefficient alpha are given. Both models have a linear form and can be solved by using a branch-and-bound algorithm. The first model assumes an item bank calibrated under the Rasch model and can be used, for instance, when classical test theory has to serve as an…

A reduction in agricultural activity in a rural farming community will result in reduced activity in almost every sector of the local economy. The result may be measured in loss of employment and income. This report provides a method to estimate such economic impacts with a minimum of data collection and manipulation. Most of the input data…

The relationship between analysis of variance (ANOVA) methods and their analogs (analysis of covariance and multiple analyses of variance and covariance--collectively referred to as OVA methods) and the more general analytic case is explored. A small heuristic data set is used, with a hypothetical sample of 20 subjects, randomly assigned to five…

This paper presents a fixed effects model on the impact of individual high schools on adult earnings. This model not only captures the effects on observed and unobserved characteristics of high school on earnings, but also can control for selection bias resulting from correlation between school quality and student ability. The principal data used…

Meta-analysis is a technique for combining the summary statistics from previously conducted research studies to indicate the direction of results and provide an index of the magnitude of effect size. This paper focuses on the effect of the violation of the assumption of independence (that the value of any included statistic is in no way…

This collection of materials includes six units dealing with applications of matrix methods. These are: 105-Food Service Management; 107-Markov Chains; 108-Electrical Circuits; 109-Food Service and Dietary Requirements; 111-Fixed Point and Absorbing Markov Chains; and 112-Analysis of Linear Circuits. The units contain exercises and model exams,…

In the last decade, a modeling technique has been developed to handle complex input/output analyses where outputs involve joint products and there are no known mathematical relationships linking the outputs or inputs. The technique uses the geometrical concept of a six-dimensional shape called a polytope to analyze the efficiency of each…

A study was undertaken to develop guidelines for the interpretation of the parameters of three multidimensional item response theory models and to determine the relationship between the parameters and traditional concepts of item difficulty and discrimination. The three models considered were multidimensional extensions of the one-, two-, and…

This discussion of how the multilevel character of data should influence analyses of the determinants of educational achievement is grounded in the context of planning explanatory analyses for the longitudinal Second International Mathematics Study (SIMS). The intention is to describe how a multilevel perspective in the specification of…

Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as…

The development of new statistical methods of log-linear models by Leo Goodman has led to major advances in the statistical analysis of categorical data. Goodman's logit analysis, (the simplest form of log-linear models) can be applied in evaluation studies to estimate the "main effects" and "interaction effects" of categorical…

A description of the development and application of a hierarchical/binary model by which a curriculum may be analyzed to determine alternative instructional sequences given particular instructional objectives and limiting constraints forms the body of this report. The background of the project as part of an effort by the U.S. Navy Recruiting…

Although there is a healthy trend toward employment of multivariate statistical methods in the analysis of data from experiments in psychology and education which involve multiple dependent variables, there remains a need to demonstrate the wide variety of data analytic techniques available for post hoc analysis of statistically significant…

Working in groups of three, seventh-grade students were video taped solving an applied mathematical problem. Audio tapes were made of each group discussing their session. Analysis focused on the first stage of Noddings (1984) model of problem solving for school mathematics: Creation of a representation. Some factors identified as impeding…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…