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…

The mathematical extension from scalars to matrices as a prerequisite for univariate to multivariate generalizations of statistical concepts and methods is discussed. One reason for several alternative techniques is the multitude of ways to generalize from univariate concepts to multivariate concepts. The additional complexity, and lack of…

A computer-simulated study was made of the sampling distribution of omega squared, a measure of strength of relationship in multivariate analysis of variance which had earlier been proposed by the author. It was found that this measure was highly positively biased when the number of variables is large and the sample size is small. A correction…

The basic notion of variability is generalized from a univariate context to a multivariate context using two matrix functions, a determinant, and a trace, yielding a number of alternative multivariate indices of shared variation. Some problems in the interpretation of tests of multivariate hypotheses are reviewed. (Author/BW)

The use of characteristic coding (dummy coding) is made in showing solutions to four multivariate problems using canonical analysis. The canonical variates can be themselves analyzed by the use of multiple linear regression. When the canonical variates are used as criteria in a multiple linear regression, the R2 values are equal to 0, where 0 is…

Type I error rates of four multivariate tests (Pilai-Bartlett trace, Johansen's test, James' first-order test, and James' second-order test) were compared for heterogeneous covariance matrices in 360 simulated experiments. The superior performance of Johansen's test and James' second-order test is discussed. (SLD)

This investigation examined the effectiveness of training Japanese and American children with a visual animation/construction or verbal labelling strategy for solving computerized geometric matrices that were correctly or incorrectly completed and varied in number of elements (l to 3) and number of transformations (0 to 2). Subjects were 209…