Date of Award
Master of Arts in Psychology
Wayne F. Velicer
A variety of rules have been suggested for determining the number of observations 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 empirical or theoretical rationale. In 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 (aij) 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 when the sample component pattern was well defined (aij = .80). Sample component patterns possessing moderate component saturation (.60) provided a good fit to the population pattern across conditions when sample size was greater than or equal to 150 observations. Weakly defined sample component patterns (aij = .40, low p/m ratio) provided a good match when sample size was in the range of 300 to 400 observations.
Guadagnoli, Edward, "The Relationship of Sample Size to the Stability of Component Patterns: A Simulation Study" (1984). Open Access Master's Theses. Paper 1575.