method note
How large a sample does factor analysis need
What sample size is needed for factor analysis and SEM?
The 5–10 respondents per item rule is common but misleading; what matters is not headcount but the size of the loadings and the number of items per factor. With high loadings (≥.80) and 4+ items per factor, around 150 may suffice; with weak loadings and sparse factors, 300–500 may be needed. For SEM, 200 is the usual floor.
Why ratio rules fall short
A respondent-per-item ratio ignores the quality of the instrument. A well-defined structure with strong loadings emerges stably even in a small sample; a poorly defined one will not settle with thousands. The decision is about the instrument before it is about the sample.
A practical approach
A power analysis based on expected effect size, model complexity and target power is more defensible than any rule of thumb. For SEM, 5–10 observations per free parameter to be estimated is a workable reference.
The work behind this note
- Factor Analysis and Validity in Social Sciences: Application of Exploratory and Confirmatory Factor Analyses2017 · 2,435 citations
- Structural Equation Modeling (SEM) for Social and Behavioral Sciences Studies: Steps Sequence and Explanation2024 · 44 citations
- How and When to Use Which Fit Indices? A Practical and Critical Review of the Methodology2020 · 132 citations
Other method notes
- Exploratory or confirmatory? Which factor analysis, and whenShould I use exploratory or confirmatory factor analysis?
- Which fit index to report, and whenWhich fit indices should I report in structural equation modelling?
- Validity and reliability: what to report, and howHow are validity and reliability reported, and how do they differ?
Written for researchers and graduate students. Conventions described here are conventions, not rules — check them against your own design before you report.