Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General

Adequate statistical power contributes to observing true relationships in a dataset. With a thoughtful power analysis, the adequate but not excessive sample could be detected. Therefore, this paper reviews the issue of what sample size and sample power the researcher should have in the EFA, CFA, and SEM study. Statistical power is the estimation of the sample size that is appropriate for an analysis. In any study, four parameters related to power analysis are Alpha, Beta, statistical power and Effect size. They are prerequisites for a priori sample size determination. Scale development in general and Factor Analysis (EFA, CFA) and SEM are large sample size methods because sample affects precision and replicability of the results. However, the existing literature provides limited and sometimes conflicting guidance on this issue. Generally, for EFA the stronger the data, the smaller the sample can be for an accurate analysis. In CFA and SEM parameter estimates, chi-square tests and goodness of fit indices are equally sensitive to sample size. So the statistical power and precision of CFA/SEM parameter estimates are also influenced by sample size. In this work after reviewing existing sample power analysis rules along with more elaborated methods (like Monte Carlo simulation), we conclude with suggestions for small samples in factor analysis found in literature.