Covariance structure analytic techniques have become increasingly popular in recent years. During this period, users of statistical software packages have become more and more sophisticated, and more and more researchers are wanting to make sure that they are using the "best" statistic, whether it be for small sample considerations or…

Different ways that dependent variables can cause multivariate significance are illustrated. It is argued that univariate tests should not be used as follow-up procedures to identify the variables that can contribute to multivariate significance. Methods that can be used to determine the contributions individual variables make to multivariate…

Multivariate methods are being used with increasing frequency in educational research because these methods control "experimentwise" error rate inflation, and because the methods best honor the nature of the reality to which the researcher wishes to generalize. This paper: explains the basic logic of canonical analysis; illustrates that…

Several important issues related to canonical correlation have been recognized and resolved during the last several years. The purpose of this presentation is to offer an organized, comprehensive, and current annotated bibliography of the many recent developments and extensions of canonical methods. The bibliography does not emphasize references…

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

Generalizability or invariance procedures have been known for over three decades. Through the years, these procedures have not been widely discussed or employed. One reason for the lack of use is that most of the articles on invariance procedures have been mathematically oriented. The mathematical orientation of research articles and the lack of…

Virtually all parametric statistical procedures have been shown to be special cases of canonical correlation analysis, which is a useful research methodology particularly when augmented by the calculation of canonical structure, index, and invariance coefficients. A logic for conducting stepwise canonical correlation analysis based upon evaluation…

Methods of regression commonality analysis are generalized for use in canonical correlation analysis. An actual data set (involving educators' attitudes toward death and age, locus of control, religion, and occupational role in working with terminally ill children) is employed to illustrate the extension. The method can be applied with respect to…

A Monte Carlo study was conducted to discover the amount of bias to be expected in canonical correlations and in the canonical redundancy statistic. Six hundred random sample replications of 72 conditions were performed and the mean sample values compared with population values. Conditions were varied with respect to the number of predictor…

A scheme, using features in a cartoon-like human face to represent variables, is tested as to its ability to graphically depict multivariate data. A factor analysis of Harman's "24 Psychological Tests" was performed and yielded four orthogonal factors. Nose width represented the loading on Factor 1; eye size on Factor 2; curve of mouth…

Multivariate selection can be represented as a linear transformation in a geometric framework. In this note this approach is extended to describe the effects of selection on regression analysis and to adjust for the effects of selection using the inverse of the linear transformation. (Author/BW)

Canonical correlation analysis and application of double-cross validation procedures provided evidence of significant shared variance between the Preprofessional Skills Test and the American College Test scores of 537 education majors, questioning the need for students to take both tests. (Author/CB)

Describes the method of discriminant analysis, including the concept of discriminant function, discriminant score, group centroid, and discriminant weights and loadings. Discusses methods for testing the statistical significance of a function, methods of using the function in classification, and the concept of rotating functions. Illustrates the…

Provides an example to illustrate the clustering approach. Discusses the variety of approaches in clustering; choice of cluster analytic techniques; the steps in cluster analysis; the data features such as level, shape, and scatter, that affect cluster results; alternate clustering methods and their relative effectiveness; and applications of…

The study attempted to determine if there are differences in the perception of male and female managers toward communication barriers. Data were collected from 156 managers and analyzed using a multivariate analysis of variance (sex and salary level). Results showed significant differences in perceptions among male and female managers. (Author/CH)