Two types of questions may be asked in educational inquiry: educological ones--those seeking descriptions of educational events, and programmatic ones--those seeking prescriptions for educational interventions. Quantitative educology is described as consisting of three branches: the philosophy, science, and praxiology of education. The SIGGS…

Measures of multivariate association, based on Wilks'"lambda" or the Bartlett-Nanda-Pillai trace criterion "V", are compared in terms of properties of univariate R-squared, which they generalize. A unified set of derivations of properties is provided, which is self-contained and not restricted to decompositions in canonical…

Correspondence analysis (CA) aids analysis of residuals from independence models and decomposes the departure from independence in a two-way contingency table. CA of incomplete tables is proposed that decomposes the departure from the quasi-independence model. This procedure is equivalent to the French procedure for missing data--reconstitution of…

With reference to the authors' previous paper (1985), it is proposed that loglinear analysis can be used to detect interactions in a multiway contingency table and explore the form of these interactions with correspondence analysis. Correspondence analysis assists in finding a model with restrictions on the interaction parameters. (TJH)

Analyzed are the different stages in the conceptual evolution of infinity as developed historically through the work of Bolzano and Cantor. Results of a study of 18 to 20 year old's concept of infinity prior to instruction produced aspects of the passage between conceptual levels of infinity. (MDH)

Set correlation is a multivariate generalization of multiple regression/correlation analysis that features the employment of overall measures of association interpretable as proportions of variance and the use of set-partialled sets of variables. The statistical development of the theory and several examples are presented. (Author/JKS)

Develops and analyzes four algorithms for feature selection in the context of rough set methodology. Experimental results confirm the expected relationship between the time complexity of these algorithms and the classification accuracy of the resulting upper classifiers. When compared, results of upper classifiers perform better than lower…

The use of the systems approach in educational inquiry is not new, and the models of input/output, input/process/product, and cybernetic systems have been widely used. The general systems model is an extension of all these, adding the dimension of environmental influence on the system as well as system influence on the environment. However, if the…

Analysis of (n=92) university students' construction of visual representations (Venn diagrams) of eight set expressions found competent and error-prone students constructed and used procedures to complete set translation tasks, and two-thirds of observed errors arose from consistent implementation of ill-formed procedures. (Author/MKR)

L. A. Goodman's loglinear formulation for bi-way contingency tables is extended to tables with or without missing cells and is used for exploratory purposes. Three-way tables and generalizations of correspondence analysis are deduced, and a generalized version of Goodman's algorithm is used to estimate scores in all cases. (Author/TJH)

Presents a manually constructed knowledge representation aimed at increasing the effectiveness of information retrieval systems. The framework of first order theories is used to analyze the properties of this new structure. The analysis demonstrates that the retrieval function takes term dependencies into account and distinguishes between…

Homogeneity analysis (multiple correspondence analysis), which is usually applied to "k" separate variables, was applied to sets of variables by using sums within sets. The resulting technique, OVERALS, uses optimal scaling. The corresponding OVERALS computer program minimizes a least squares loss function via an alternating least…

This paper contains an elementary and short proof for the case that the underlying distribution function F is discrete, and then extends the result to the general F. In other proofs underlying iid sequences of random variables with continuous distributions are considered to be the "ideal" case. In this paper discretization of the underlying iid…

A theoretical basis was formulated for a model of individualized instruction. The theory is semi-axiomatic in nature so that the definitions and assumptions used are stated explicitly. Set theory and symbolic logic are the conceptual tools used. The model includes theories of subject-matter structure and student state description. These are…

Describes rough sets theory and discusses the advantages it offers for information retrieval, including the implicit inclusion of Boolean logic, term weighting, ranked retrieval output, and relevance feedback. Rough set formalism is compared to Boolean, vector, and fuzzy models of information retrieval and a small scale evaluation of rough sets is…