James H. Steiger

Tests for comparing elements of a correlation matrix.

In a variety of situations in psychological research, it is desirable to be able to make statistical comparisons between correlation coefficients measured on the same individuals. For example, an experimenter may wish to assess whether two predictors correlate equally with a criterion variable. In another situation, the experimenter may wish to test the hypothesis that an entire matrix of correlations has remained stable over time. The present article reviews the literature on such tests, points out some statistics that should be avoided, and presents a variety of techniques that can be used safely with medium to large samples. Several illustrative numerical examples are provided.

ON THE MULTIVARIATE ASYMPTOTIC DISTRIBUTION OF SEQUENTIAL CHI-SQUARE STATISTICS

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-squaredifference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided.

Beyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis.

This article presents confidence interval methods for improving on the standard F tests in the balanced, completely between-subjects, fixed-effects analysis of variance. Exact confidence intervals for omnibus effect size measures, such as or and the root-mean-square standardized effect, provide all the information in the traditional hypothesis test and more. They allow one to test simultaneously whether overall effects are (a) zero (the traditional test), (b) trivial (do not exceed some small value), or (c) nontrivial (definitely exceed some minimal level). For situations in which single-degree-of-freedom contrasts are of primary interest, exact confidence interval methods for contrast effect size measures such as the contrast correlation are also provided.

The insidious effects of failing to include design-driven correlated residuals in latent-variable covariance structure analysis.

In practice, the inclusion of correlated residuals in latent-variable models is often regarded as a statistical sleight of hand, if not an outright form of cheating. Consequently, researchers have tended to allow only as many correlated residuals in their models as are needed to obtain a good fit to the data. The current article demonstrates that this strategy leads to the underinclusion of residual correlations that are completely justified on the basis of measurement theory and research design. In many designs, the absence of such correlations will not substantially harm the fit of the model; however, failure to include them can change the meaning of the extracted latent variables and generate potentially misleading results. Recommendations include (a) returning to the full multitrait-multimethod design when measurement theory implies the existence of shared method variance and (b) abandoning the evil-but-necessary attitude toward correlated residuals when they reflect intended features of the research design.

A note on multiple sample extensions of the RMSEA fit index

Generalization of the Steiger‐Lind root mean square error of approximation fit indexes and interval estimation procedure to models based on multiple independent samples is discussed. In this article, we suggest an approach that seems both reasonable and workable, and caution against one that definitely seems inappropriate.

A 12-Point Circumplex Structure of Core Affect

Core Affect is a state accessible to consciousness as a single simple feeling (feeling good or bad, energized or enervated) that can vary from moment to moment and that is the heart of, but not the whole of, mood and emotion. In four correlational studies (Ns = 535, 190, 234, 395), a 12-Point Affect Circumplex (12-PAC) model of Core Affect was developed that is finer grained than previously available and that integrates major dimensional models of mood and emotion. Self-report scales in three response formats were cross-validated for Core Affect felt during current and remembered moments. A technique that places any external variable into the 12-PAC showed that 29 of 38 personality scales and 30 of 30 mood scales are significantly related to Core Affect, but not in a way that revealed its basic dimensions.

Empirical and conceptual problems with longitudinal trait-state models: introducing a trait-state-occasion model.

The latent trait-state-error model (TSE) and the latent state-trait model with autoregression (LST-AR) represent creative structural equation methods for examining the longitudinal structure of psychological constructs. Application of these models has been somewhat limited by empirical or conceptual problems. In the present study, Monte Carlo analysis revealed that TSE models tend to generate improper solutions when N is too small, when waves are too few, and when occasion factor stability is either too large or too small. Mathematical analysis of the LST-AR model revealed its limitation to constructs that become more highly auto-correlated over time. The trait-state-occasion model has fewer empirical problems than does the TSE model and is more broadly applicable than is the LST-AR model.

Nonholistic processing in mental rotation: some suggestive evidence.

A series of experiments, using a modification of the Shepard and Metzler mental rotation task, was performed to investigate Shepard’s “holistic rotation” hypothesis. Effective figural complexity was manipulated in the experiments in two distinct ways. In one manipulation, blocks were added to the standard 10-blockfigures. In the other manipulation, the figures used and the direction of angular rotation were restricted so that some featural information in the figures was redundant, that is, unnecessary for the discrimination task at hand. There were two major conclusions. First, when figural complexity is effectively manipulated, it has a powerful effect on the “speed of mental rotation,” as measured by the slope of the curve relating reaction time to angular disparity. Second, it is possible, by ignoring featural redundancy, to construct experimental paradigms in which “complexity” of figures is apparently manipulated but has no effect on speed of mental rotation. This fact provides a possible explanation of why some previous experiments have failed to find a complexity effect in mental rotation.

Factor indeterminacy in the 1930's and the 1970's some interesting parallels

The issue of factor indeterminacy, and its meaning and significance for factor analysis, has been the subject of considerable debate in recent years. Interestingly, the identical issue was discussed widely in the literature of the late 1920s and early 1930s, but this early discussion was somehow lost or forgotten during the development and popularization of multiple factor analysis. There are strong parallels between the arguments in the early literature, and those which have appeared in recent papers. Here I review the history of this early literature, briefly survey the more recent work, and discuss these parallels where they are especially illuminating.

Creativity and Technical Innovation Spatial Ability’s Unique Role

In the late 1970s, 563 intellectually talented 13-year-olds (identified by the SAT as in the top 0.5% of ability) were assessed on spatial ability. More than 30 years later, the present study evaluated whether spatial ability provided incremental validity (beyond the SAT’s mathematical and verbal reasoning subtests) for differentially predicting which of these individuals had patents and three classes of refereed publications. A two-step discriminant-function analysis revealed that the SAT subtests jointly accounted for 10.8% of the variance among these outcomes (p < .01); when spatial ability was added, an additional 7.6% was accounted for—a statistically significant increase (p < .01). The findings indicate that spatial ability has a unique role in the development of creativity, beyond the roles played by the abilities traditionally measured in educational selection, counseling, and industrial-organizational psychology. Spatial ability plays a key and unique role in structuring many important psychological phenomena and should be examined more broadly across the applied and basic psychological sciences.