The goodness-of-fit of correlational pattern hypotheses has traditionally been assessed either with a likelihood ratio statistic or with a quadratic form statistic. Several alternative statistics, based on the use of the Fisher r-to-z transform, are proposed and assessed in a Monte Carlo experiment. (Author/JKS)

A commentary is made on a previously published article concerning testing the equivalence of covariance matrices. An error in the previous article (by the same authors) is pointed out and the consequences of the error are discussed. (JKS)

A method is proposed and illustrated for estimating the degree to which a factor rotation to a hypothesized target represents an improvement over rotation to a random target. (Author)

The logic and procedures underlying a disturbance term regression test of logical consistency for structural models are reviewed for recursive and nonrecursive designs. It is shown that in a simple three-variable, complete mediational case the test procedure is mathematically equivalent to a part correlation. (Author/LMO)

The strategy for investigating convergent and discriminant test validity, known as the multitrait-multimethod matrix, is investigated. A nonparametric significance testing procedure is suggested and demonstrated. (JKS)

A general statistical model for the multivariate analysis of mean and covariance structures is described. Matrix calculus is used to develop the statistical aspects of one new special case in detail. This special case separates the confounding of principal components and factor analysis. (DEP)