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1. Multivariate Cluster Analysis.

Author

McGraw-Hill Book Co., Monterey, CA. and McRae, Douglas J.

Abstract

Procedures for grouping students into homogeneous subsets have long interested educational researchers. The research reported in this paper is an investigation of a set of objective grouping procedures based on multivariate analysis considerations. Four multivariate functions that might serve as criteria for adequate grouping are given and discussed; a method for optimizing these functions is also described. The set of procedures is illustrated through application to data from two samples of students, each student with scores on either ten or eleven subtests of a criterion referenced mathematics inventory. The results indicate that the procedures discussed provide a promising means for grouping students to minimize classroom heterogeneity. (Author)

Published
1971

2. Technique for Approximating the Bivariate Normal Correlation Coefficient, Rho, and Estimating Tetrachoric r.

Author

Educational Testing Service, Princeton, NJ. and Kirk, David B.

Abstract

In this paper a reliable method is found for approximating the value of the Bivariate Normal Correlation Coefficient, rho, given values of the joint probability and the normal deviates, h and k, or the related areas. This technique finds useful application in the computation of the tetrachoric correlation coefficient, r, when the underlying distributions may be assumed to be normal. (Author)

Published
1971

3. An Artificial Intelligence Approach to the Symbolic Factorization of Multivariable Polynomials. Technical Report No. CS74019-R.

Author

Virginia Polytechnic Inst. and State Univ., Blacksburg. Dept. of Computer Science. and Claybrook, Billy G.

Abstract

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 automatic classification) in an attempt to reduce the amount of searching for the irreducible factors of the polynomial. The approach taken to polynomial factorization is quite different from previous attempts because: (1) it is distinct from numerical techniques; (2) possibilities for terms in a factor are generated from the terms in the polynomial; and (3) a reclassification technique is used to allow the application of different sets of heuristics to a polynomial during factorization attempts on it. Data presented show the importance of learning to the efficiency of operation of the scheme. Factorization times of polynomials factored by both the scheme described in this paper and Wang's implementation of Berlekamp's algorithm are given and compared, and an analysis of avariance experiment provides an indication of the significant sources of variation influencing the factorization time. (Author/DGC)

Published
1974