The factor analysis literature includes a range of recommendations regarding the minimum sample size necessary to obtain factor solutions that are adequately stable and that correspond closely to population factors. A fundamental misconception about this issue is that the minimum sample size, or the minimum ratio of sample size to the number of variables, is invariant across studies. In fact, necessary sample size is dependent on several aspects of any given study, including the level of communality of the variables and the level of overdetermination of the factors. The authors present a theoretical and mathematical framework that provides a basis for understanding and predicting these effects. The hypothesized effects are verified by a sampling study using artificial data. Results demonstrate the lack of validity of common rules of thumb and provide a basis for establishing guidelines for sample size in factor analysis.In the factor analysis literature, much attention has be;;n given to the issue of sample size. It is widely understood that the use of larger samples in applications of factor analysis tends to provide results such that sample factor loadings are more precise estimates of population loadings and are also more stable, or les s variable, across repeated sampling. Despite general agreement on this matter, there is considerable di'/ergence of opinion and evidence about the question of how large a sample is necessary to adequately acnieve these objectives. Recommendations and findings about this issue are diverse and often contradictory. The objectives of this article are to provide a

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The Personal Style Inventory (PSI) was developed to assess individuals' levels of sociotropy and autonomy, two personality characteristics considered to be associated with increased vulnerability to depression. This study used the approach of latent means analysis (LMA) within the framework of structural equation modeling (SEM) to explore the factor structure and gender differences associated with the PSI in a sample of Korean undergraduates (N = 508). Results of the confirmatory factor analysis are consistent with previous work and support the cross-cultural stability of the PSI factor structure. However, in contrast to previous research, results of the LMA showed women to have higher scores than men on sociotropy and autonomy dimensions, raising the possibility of cross-cultural differences in the interaction between these personality styles and vulnerability to depression.

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Extending earlier work by MacCallum, Browne, and Sugawara (1996), procedures are shown for conducting power analysis of tests of overall fit of covariance structure models when null and alternative levels of model fit are specified in terms of values of the GFI or AGFl fit indexes. Results show that for GFI-based power analyses, holding null and alternative values of GFI fixed, power decreases as degrees of freedom increase, which is a counter-intuitive and undesirable phenomenon indicating lower power for detecting false null hypotheses about simpler models. For AGFI-based analyses, power increases as degrees of freedom increase. However, for both indexes it is shown that it is problematic to establish consistently appropriate values for null and alternative hypotheses about model fit. Because of these problems, it is recommended that the RMSEA index is preferable as a basis for power analysis and model evaluation.