A variety of rules have been suggested for determining the sample size required to produce a stable solution when performing a factor or component analysis. The most popular rules suggest that sample size be determined as a function of the number of variables. These rules, however, lack both empirical support and a theoretical rationale. We used a Monte Carlo procedure to systematically vary sample size, number of variables, number of components, and component saturation (i.e., the magnitude of the correlation between the observed variables and the components) in order to examine the conditions under which a sample component pattern becomes stable relative to the population pattern. We compared patterns by means of a single summary statistic, g² , and by means of direct pattern comparisons using the kappa statistic. Results indicated that, contrary to the popular rules, sample size as a function of the number of variables was not an important factor in determining stability. Component saturation and absolute sample size were the most important factors. To a lesser degree, the number of variables per component was also important, with more variables per component producing more stable results.

Factor analysis or component analysis is typically used by the researcher who wishes to reduce a set of observed variables, p, to a new, smaller set of variables. This smaller set of new variables (m), labeled factors or components, depending on the method used, preserves most of the information present in the original set of variables and is a more parsimonious representation. The purpose of an analysis may be the replacement of the p scores with m factor or component scores or the interpretation of the p × m pattern of loadings, that is, correlations between the p observed variables and the m factors or components. The latter is intended to facilitate the understanding of the relations that exist between the observed variables.

A major issue involves determining the number of independent observations (N) required...