| This study investigated the applicability of Ke's (2001) findings regarding the relationships among the sample size, the number of variables, the number of factors, and the level of communality in exploratory factor analysis to a live dataset. A second purpose was to extend Ke's findings, obtained only for maximum likelihood analysis (MLFA), to principal factor analysis (PFA) and principal component analysis (PCA). To accomplish these purposes, live data from a large dataset consisting of 9468 observations from the Millon Clinical Multiaxial Inventory-III (MCMI-III) were factor analyzed using MLFA, PCA, and PFA. Three methods were employed to determine the number of factors to be extracted. Additionally, a variety of factor conditions were generated from the live data to create subpopulation conditions with varying numbers of factors and variable to factor ratios. Random samples were repeatedly drawn from the population and subpopulation conditions. Coefficients of congruence between the population/subpopulation and sample solutions were determined for three values of congruence (0.92, 0.95, and 0.98). The results were then compared with Ke's (2001) guidelines for the minimum sample size needed for factor analysis. Three major findings emerged. First, when the factor structure was well defined, Ke's (2001) guidelines were conservative. Second, when the factor structure was poorly defined, the minimum required sample sizes observed were close to, but inconsistent with, Ke's guidelines. Third, the minimum sample sizes needed to obtain good, very good, and excellent congruence were comparable among MLFA, PCA, and PFA. Additionally, the minimum sample size was influenced by the number of factors retained, the similarity in the number of variables loading on each factor, the number of variables sharing loadings on more than one factor, and underfactoring and overfactoring the data. Based on factor analysis of one live dataset and subpopulations from that dataset, Ke's guidelines may provide a conservative estimate for the minimum sample sizes needed for good and excellent congruence. |
