Sample size in factor analysis.

Abstract

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

The Impact of Event Scale-Revised: Psychometric properties in a sample of motor vehicle accident survivors

“…These authors argue against the use of invariant rules for determination of sample size for a CFA and instead, present a mathematical framework for computing the necessary sample size based on the size and variability of the obtained communalities and whether factors are overdetermined. In the case of the present data, with five or more items per factor, moderate to high expected communalities based on past exploratory factor analyses, and n = 182, the approximate value of the congruence coefficient (which reflects the degree of correspondence between sample and population factors) is .98, which is excellent within MacCallum et al▯s (1999) framework. Thus, the sample size in the present report is adequate for a CFA.…”

Investigating population heterogeneity with factor mixture models.

“…An adequate sample size depends on several different factors, including the number of classes, the restrictiveness of the within-class model, the withinclass model complexity, the quality of covariates, and the reliability of the observed data within class. This situation is not different from common factor analysis, in which MacCallum, Widaman, Zhang, and Hong (1999) have shown that simple rules of thumb for the minimum sample size needed for the recovery of factors are inappropriate because an adequate sample size depends strongly on characteristics of the variables and the study design. Note.…”

On the validity and generality of transfer effects in cognitive training research

“…1). Of note for the focus of the present review, sample sizes of fewer than 45 participants are generally insufficient to fit common factor models (MacCallum, Widaman, Zhang, & Hong, 1999).…”