Estimates of the internal consistency and reliability of the first principal component are provided through the use of the largest characteristic root and associated vector of the equicorrelation matrix. The estimate of the internal consistency is also shown to be a lower bound for the measure provided by Horn (1969). (Author)

The fundamental problems that ipsative measures impose for factor analysis are shown analytically. Normative and ipsative correlation matrices are used to show that the factor pattern induced by ipsativity will overwhelm any factor structure seen with normative factor analysis, making factor analysis not interpretable. (SLD)

The problem of combining information to estimate standardized partial regression coefficients in a linear model is considered. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. This estimate can be generalized to address situations in which not every study measures every…

The purpose of this paper is to examine the validity of regression estimates when skewed dichotomous scales are used as independent variables. When Pearson product-moment correlations are used to measure zero-order associations involving dichotomous variables, the resulting coefficients underestimate the true associations. As a result, using…

A recurring problem in educational research is how to account for non-random selection that has restricted the range of the variables of interest in correlational analyses. Several expressions due to H. Pearson (1903) and presented in matrix notation by D. N. Lawley (1943-44) are commonly used in selection settings to adjust for samples chosen on…

The relationship of sample size to number of variables in the use of factor analysis has been treated by many investigators. In attempting to explore what the minimum sample size should be, none of these investigators pointed out the constraints imposed on the dimensionality of the variables by using a sample size smaller than the number of…

Principal components analysis is generalized to the case where any of the variables under consideration can be nominal, ordinal or interval. Hotelling's original formulation is seen to be a special case of this generalization. (JKS)

A computer program which creates and stores a cumulative item covariance matrix upon each administration of an instrument is described. Use of this program would facilitate keeping a constant log on reliability in situations in which the test is administered to different groups over a period of time. (Author/JKS)

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

Structural models that yield circumplex inequality patterns are reviewed, focusing on a model developed by T. W. Anderson (1960). A modification is proposed to this model to allow for negative correlations. This model may be reparameterized as a factor analysis model with nonlinear constraints on the factor loadings. (SLD)

An equal-level approach is proposed for investigating multitrait-multimethod (MTMM) matrices with respect to other organizational units that contain additional information concerning a MTMM matrix's validity. The approach requires equality in "data level" before coefficients are submitted for evaluation. Disaggregation is central to…

Reanalysis with updated exploratory and confirmatory factor analytic methods of correlation matrices for 21 structure-of-intellect divergent production tests from the University of Southern California Aptitude Research Project suggests that the results cannot be replicated and support a higher order 2-factor oblique model of covariance among test…

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

To examine whether the Roma (Gypsy) population of Serbia, like other South Asian population groups, average lower than Europeans on "g", the general factor of intelligence, we tested 323 16- to 66-year-olds (111 males; 212 females) in three different communities over a two-year-period on the Raven's Colored and/or Standard Progressive…

This paper discusses the issue of multiple testing and overall Type I error rates in contexts other than multiple comparisons of means. It demonstrates, using a 5 x 5 correlation matrix, the application of 5 recently developed modified Bonferroni procedures developed by the following authors: (1) Y. Hochberg (1988); (2) B. S. Holland and M. D.…