Exploratory Factor Analysis With Small Sample Sizes

Area of Science:

• Psychometrics
• Statistical analysis
• Behavioral science

Background:

• Exploratory Factor Analysis (EFA) is typically recommended for large sample sizes (N ≥ 50).
• Limited research exists on the minimum sample size requirements for EFA in behavioral research.
• Understanding sample size effects is crucial for accurate data interpretation.

Purpose of the Study:

• To determine the minimum sample size (N) for reliable EFA results when N < 50.
• To investigate the influence of factor loadings (λ), number of factors (f), and variables (p) on EFA reliability.
• To assess the impact of common data distortions on EFA with small sample sizes.

Main Methods:

• Conducted simulation studies to estimate minimum N under varying conditions (λ, f, p).
• Examined the robustness of small N EFA to interfactor correlations, model error, secondary loadings, unequal loadings, and unequal p/f ratios.
• Assessed factor recovery using pattern congruence coefficients, factor score correlations, Heywood cases, and eigenvalue gaps.
• Performed a subsampling study on a psychological dataset (Big Five Inventory).

Main Results:

• EFA can produce reliable results for N < 50 when data are well-conditioned (high λ, low f, high p).
• Small sample sizes can sustain minor data distortions without significantly compromising EFA quality under favorable conditions.
• Simulation results provide specific guidelines for minimum N based on data characteristics.
• Empirical validation on a psychological dataset supports the simulation findings.

Conclusions:

• EFA can be reliably applied to datasets with N < 50 under specific, favorable conditions.
• Researchers should consider factor loadings, number of factors, and variables when assessing sample size adequacy for EFA.
• The findings challenge the conventional minimum sample size rule for EFA in behavioral research.