The Relationship of Sample Size to the Stability of Component Patterns: A Simulation Study

A variety of rules have been suggested for determining the number of observations required to produce a stable solution when performing a factcr 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 empirical or theoretical rationale. Ill order to more precisely examine the conditions under which a sample component pattern becomes stable relative to its population pattern, the effect of number of variables (p), number of components (m), and component saturation (a;j) were examined in addition to the effect of sample size (N). Computer simulated sample component patterns were compared to population component patterns by means of a single summary statistic, g, and by direct comparison of the patterns in terms of salient and non-salient component loading identification. Results indicate that the number of variables is not an important factor in determining an acceptable level of comparability between patterns. Component saturation and to a lesser degree, sample size and the number of variables per component, surfaced as important factors. A good match to the population pattern vas attained across all conditions vhen the sample component pattern was well defined (a . . = lJ • 80). Sample component patterns possessing moderate component saturation (.60) provided a good fit to the population pattern across conditions when sample size was