Univariate procedures proposed by M. Brown and A. Forsythe (1974) and the multivariate procedures from D. Nel and C. van der Merwe (1986) were generalized to form five new multivariate alternatives to one-way multivariate analysis of variance (MANOVA) for use when dispersion matrices are heteroscedastic. These alternatives are evaluated for Type I…

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…

The method of unweighted means (MUM) was studied to determine Type I error rates associated with various degrees of imbalance among the cell frequencies. Conditions under which the MUM is a reasonable alternative to the least squares method are discussed, and the issue of power is considered. (SLD)

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…

Interpretations of relative variable importance in multivariate analysis of variance are discussed, with attention to (1) latent construct definition; (2) linear discriminant function scores; and (3) grouping variable effects. Two numerical ranking methods are proposed and compared by the bootstrap approach using two real data sets. (SLD)

Some interpretations of relative variable importance in the contexts of multivariate analysis of variance (MANOVA) and discriminant analysis (DA) are presented. Some indices potentially useful for the interpretations are presented, and the assessment of variable importance is illustrated using real data sets. Both descriptive discriminant analysis…

A Monte Carlo study was conducted using the Statistical Analysis System IML computer program to compare the multivariate analysis of variance (MANOVA) simultaneous test procedures of Roy's Greatest Root, the Pillai-Bartlett trace, the Hotelling-Lawley trace, and Wilks' lambda, in terms of power and Type I error under various conditions, including…

Set correlation is explored as an option in analysis of two-way contingency tables. It includes measures of strength of association, significance tests and estimation, power analysis, and computer programs. (SLD)

Three alternative solutions available for analysis of variance (ANOVA) using two-way and three-way completely randomized factorial designs with disproportional cell sizes across all two-way and three-way summary tables with no empty cells are discussed. These solutions are categorized as unique, sequential, and experimental. The procedures used,…

Calls attention to limitations and dangers in routine application of multivariate analysis of variance (MANOVA), describes some alternative procedures, and laments the necessarily pervasive character of the statistical problem. (Author)

Multivariate and univariate analysis of variance methods (MANOVA and ANOVA, respectively) are compared for their relative value in educational research. The favoritism shown multivariate techniques is questioned. Criteria for the selection of the appropriate technique are outlined. The relationships among research hypotheses, statistical…

This Monte Carlo study examines whether, given various numbers of variables, treatments, and sample sizes, in a one-way multivariate analysis of variance, Type I error rates of the test approximations provided by the BMDP program, the Statistical Analysis System (SAS), and the Statistical Package for the Social Sciences (SPSS) for Roy's largest…

Conventional statistical significance tests do not inform the researcher regarding the likelihood that results will replicate. One strategy for evaluating result replication is to use a "bootstrap" resampling of a study's data so that the stability of results across numerous configurations of the subjects can be explored. This paper…

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…