Matrix differencing of data vectors is introduced as a method for computing test variance and is compared to traditional analysis of variance. Applications for computer assisted instruction, provided by supplemental computer software, are also described. (Author/GDC)

The multiplicative correction term for the degrees of freedom in a repeated measures analysis of variance table is given for the cases in which there is equal variability per time point, and the correlation between observations is k time units apart. This correction equals the correlation coefficient raised to the kth power. (JKS)

The distributional characteristics of the Kaiser-Rice measure of sampling adequacy (MSA) were investigated with sample correlation matrices from multivariate normal populations where the level of correlation (LC) was systematically varied. Two additional variables were manipulated--sample size (SS) and number of variables (NV). Ten matrices were…

Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.…

This paper outlines the problems associated with the estimation of variance components in generalizability analyses using analysis of variance software, and discusses the most useful software currently available for this specialist application: the MIVQUE method of the Statistical Analysis System (SAS) procedure VARCOMP. (Author)

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…

Simultaneous test procedures (STPS for short) in the context of the unrestricted full rank general linear multivariate model for population cell means are introduced and utilized to analyze interactions in factorial designs. By appropriate choice of an implying hypothesis, it is shown how to test overall main effects, interactions, simple main,…

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 Welch-James procedure may be used to test hypothesis on means, when independent samples from populations with heterogenous variances are available. Summation formulas for the Welch-James procedure are presented for the 2x2 design. Matrix formulas that permit routine application of the procedure to crossed factorial designs are presented.…

This paper describes a variety of confirmatory factor analysis models that provide improved tests of multitrait-multimethod matrices, and compares three different approaches (the original Campbell-Fiske guidelines, an analysis of variance model, and confirmatory factor analysis models). (PN)

The effects of under and overrotation on common factor loading stability under three levels of common variance and three levels or error are examined. Four representative factor matrices were selected. Results suggested that matrices which account for large amounts of common variance tend to have stable factor loadings. (Author/RL)

The multiple regression or general linear model (GLM) is a parameter estimation and hypothesis testing model which encompasses and approaches the more familiar fixed effects analysis of variance (ANOVA). The transition from ANOVA to GLM is accomplished, roughly, by coding treatment level or group membership to produce a set of predictor or…

A stepwise canonical procedure, including two selection indices for variable deletion and a rule for stopping the iterative procedure, was derived as a method of selecting core variables from predictors and criteria. The procedure was applied to simulated data varying in the degree of built in structures in population correlation matrices, number…

Several procedures proposed in the literature for the analysis of growth curves are reviewed. Particular attention is given to the current issues in this area to guide practitioners in the selection of the most appropriate methodology. (Author)

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)