Minimization of the within-cluster sums of squares (WCSS) is one of the most important optimization criteria in cluster analysis. Although cluster analysis modules in commercial software packages typically use heuristic methods for this criterion, optimal approaches can be computationally feasible for problems of modest size. This paper presents a…

All parametric methods are special cases of canonical correlation analysis and can, in fact, be performed using the canonical correlation procedures found in commonly available computer statistics packages such as the Statistical Analysis System (SAS) software. It is suggested that canonical analysis has advantages of versatility since it can…

The concept of the general linear model (GLM) is illustrated and how canonical correlation analysis is the GLM is explained, using a heuristic data set to demonstrate how canonical correlation analysis subsumes various multivariate and univariate methods. The paper shows how each of these analyses produces a synthetic variable, like the Yhat…

The use of repeated measures research designs is explored. Repeated measures designs are often advantageous and can be implemented in a variety of research settings. One of the main advantages in repeated measures designs is the control of subject variability. Other advantages are the reduction of error variance and economy in subject recruitment.…

A hypothesized data set is used to illustrate that canonical correlation analysis is a general linear model, subsuming other parametric procedures as special cases. Specific techniques included in analyses are t tests, Pearson correlation, multiple regression, analysis of variance, multivariate analysis of variance, and discriminant analysis. (SLD)

A small multivariate data set is used to illustrate the usefulness of structure coefficients when interpreting results of educational experiments. Data are analyzed using a multivariate analysis of variance (MANOVA), and results are interpreted in three different ways to determine the contribution of individual variables to prediction: (1) using…

Using a hypothetical data set of 24 cases concerning opinions on contemporary issues on which Democrats and Republicans might disagree, concrete examples are provided to illustrate that canonical correlation analysis is the most general linear model, subsuming other parametric procedures as special cases. Specific statistical techniques included…

This paper explains in user-friendly terms why multivariate statistics are so important in educational research. The basic logic of canonical correlation analysis is presented as a simple or bivariate Pearson "r" procedure. It is noted that all statistical tests implicitly involve the calculation of least squares weights, and that all…

It is recognized that parametric methods (e.g., t-tests, discriminant analysis, and methods based on analysis of variance) are special cases of canonical correlation analysis. In canonical correlation it has been argued that structure coefficients must be computed to correctly interpret results. It follows that structure coefficients may be useful…

This paper describes structural equation modeling (SEM) in comparison with another overarching analysis within the general linear model (GLM) analytic family: canonical correlation analysis. The uninitiated reader can gain an understanding of SEM's basic tenets and applications. Latent constructs discovered via a measurement model are explored and…

The present paper suggests that multivariate techniques are very important in social science research, and that canonical correlation analysis may be particularly useful. The logic of canonical analysis is explained and discussed. The necessity of using replicability/generalizability analyses is argued. It is suggested that cross-validation…

The need for using invariance procedures to establish the external validity or generalizability of statistical results has been well documented. Invariance analysis is a tool that can be used to establish confidence in the replicability of research findings. Several approaches to invariance analysis are available that are broadly applicable across…

There are advantages to using a priori or planned comparisons rather than omnibus multivariate analysis of variance (MANOVA) tests followed by post hoc or a posteriori testing. A small heuristic data set is used to illustrate these advantages. An omnibus MANOVA test was performed on the data followed by a post hoc test (discriminant analysis). A…

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…

It is argued that, given the importance and the increased use of multivariate techniques such as factor analysis and canonical correlation, students need to be made aware of multivariate methods and the appropriate ways in which they can be applied. As a general linear model that subsumes all other parametric measures, canonical correlation…