The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…

The gateway drug model is a popular conceptualization of a progression most substance users are hypothesized to follow as they try different legal and illegal drugs. Most forms of the gateway hypothesis are that "softer" drugs lead to "harder," illicit drugs. However, the gateway hypothesis has been notably difficult to…

We extended Wilson and Cleary's (1995) health-related quality of life model to examine the relationships among symptom status (Symptoms), functional health (Disability), and quality of life (QOL). Using a community sample (N = 956) of male HIV positive patients, we tested a mediation model in which the relationship between Symptoms and QOL is…

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)

Four testing procedures for establishing the number of non-zero population roots in canonical analysis are investigated. Results of a Monte Carlo study indicate that three well-established procedures were effective, and a new procedure designed to correct a supposed flaw in the other procedures was ineffective. (JKS)

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)

Study determines that solutions derived by multiple group analysis and item-total correlation analysis were generally most interpretable from a psychological perspective. It was concluded that their application to test construction is preferred over Procrustean or confirmatory maximum likelihood approaches. (RB)

Canonical correlation analysis is considered to be a general model for bivariate and multivariate statistical methods. Some problems involving assumptions and statistical tests for parameters exist for social science data. A resolution for these problems is presented by treating canonical correlation as a special case of linear structural…

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)

Many models have been proposed for examining factors from several batteries of tests. A model for such an analysis is presented which allows for maintaining the distinction among batteries. A discussion of the computational procedures is given, and examples are provided. (Author/JKS)

This paper considers the case of two predictor variables. Figures are obtained which show the regions of significance of joint regression coefficients, regression coefficients considered separately, and the multiple correlation. The intersection of these regions of significance and non-significance illustrates how the various apparent…

The partitioned-U procedure is outlined, a fundamental logical flaw in this procedure's avoidance of any direct test of the significance of the first discriminant function or largest coefficient of canonical correlation is pointed out, and two alternatives to the partitioned-U procedure are discussed. (Author/DEP)

Several general correlation patterns are shown which give exact F tests in an analysis of variance (ANOVA) procedure. They are the most general correlation patterns one can assume in a one-way and two-way layout and still have the F tests be valid. (Author/BW)

Testing homogeneity of correlations with Fisher's Z is inappropriate when correlations are themselves correlated. Suppose measurements of brain activation and performance are taken before and during a verbal memory task. Of interest are changes in activity gradients in specific regions, R1, R2, R3, and performance, V. The "correlated correlations"…