EFA Sample Size: Planning Around Loadings, Communalities, and Stability
No minimum N applies to every EFA. Structural recovery depends on item quality, indicators per factor, loadings, communalities, factor count and departures from an ideal model.
Replace 5:1 or 10:1 rules with scenario planning, allowances for unusable data, stability checks, simulation where possible and resources for independent validation.
Sample size is a planning decision
- Target
Target effect or required precision
- Model
Complexity and measurement quality
- Design
Missingness, groups and clustering
- Stability
Power, simulation and sensitivity
Conceptual diagram. No single observations-to-variables ratio guarantees adequacy.
Source: Lê Minh · Conceptual illustration, not software output.1. Why is there no universal minimum?
N = 200 may support three factors with many strong items but be inadequate for six factors with cross-loadings and low communalities. MacCallum et al. (1999) show that sample requirements depend on communality and factor overdetermination: the quality indicators identifying each factor.
Participants-per-item ratios ignore structure. Two 20-item studies differ substantially if one has four factors with five strong items each, while another has eight factors, several with only two items.
- Describe the expected model before stating a minimum N.
- Specify factor count and items per factor.
- Estimate loading and communality ranges from prior evidence or a pilot.
- Account for ordinal data, missingness and subgroups.
- Reserve resources for validation rather than putting all N into EFA.
2. Five main drivers of sample size
Mundfrom et al. (2005) simulated recommendations varying with factors, variables per factor and communality. Their findings argue against a constant ratio across designs.
| Driver | Favorable | Unfavorable |
|---|---|---|
| Communality | High and uniform | Low or uneven |
| Primary loadings | Strong | Weak |
| Items per factor | Many quality indicators | Only 2-3 indicators |
| Complexity | Few factors and cross-loadings | Many factors and cross-loadings |
| Data quality | Adequate distributions, little missingness | Sparse ordinal data, skewness and missingness |
3. Using 5:1, 10:1, N = 200 or N = 300
These values are preliminary planning aids. DeVellis and Thorpe (2022) discuss historical rules while emphasizing that N and solution quality have a more complex relationship. Larger samples help generalization, and solutions need replication on independent data.
If an initial number is required, state assumptions. For example, planned recruitment might assume 24 items, four factors, at least six items per factor, loadings from 0.55 and communalities around 0.40 or higher. Keep the number attached to its scenario.
More respondents increase precision, but cannot turn confused items or incomplete domains into good measures.
4. Communality and overdetermination affect recovery
Communality is item variance explained by common factors. Many high-communality items with clear loadings provide repeated information for recovery. Low communalities make loadings and factor counts more vulnerable to sampling error.
Overdetermination is favorable when each factor has many strong, minimally cross-loading items. MacCallum et al. (1999) show that these features can imply requirements far from fixed rules. Do not treat post-selection communalities as known beforehand; use conservative planning ranges.
5. Expected loadings and items per factor
Two-item factors are fragile because one problematic item can destabilize the factor. More items do not automatically help if wording is redundant. Seek enough varied indicators of the same concept.
Worthington and Whittaker (2006) recommend integrating content with factor analysis in scale development. With weak or uncertain expected loadings, enlarge the item pool and N rather than expecting cutoffs to rescue the solution.
| Scenario | Risk | Response |
|---|---|---|
| 4-6 strong items per factor | Lower | Still validate |
| 3 moderate-loading items | Sensitive to one weak item | Increase N and retain reserve items |
| 2 items per factor | Difficult to stabilize and confirm | Develop more items |
| Many similarly worded items | Method factor | Vary wording |
6. Ordinal Likert data and sparse cells complicate planning
Polychoric correlations help with few-category or skewed items, but estimates can be unstable with small N and empty category-pair cells. DeVellis and Thorpe (2022) note small-sample limitations. Planning must therefore consider distributions as well as item count.
If respondents tend toward high categories, estimate sparsity in the pilot. Do not collapse categories afterward merely to make estimation run. Substantively justified collapsing rules should be documented and examined in the main study.
7. When can small samples yield useful solutions?
de Winter et al. (2009) show that some strong-loading, simple, well-overdetermined structures can be recovered with small samples. This does not justify small N universally; findings depend on the simulated conditions.
Small samples require greater transparency: consider bootstrap or subsampling comparisons, inspect Heywood cases, report uncertainty and label conclusions exploratory. A favorable simulation setting is not a new universal minimum.
When loadings, communalities and structure are unknown, use conservative scenarios rather than citing one paper to legitimize an available N.
8. Sample-size planning workflow
Draw the expected structure
Specify factors, items per factor and expected correlations.
Obtain initial information
Use prior studies, a pilot or conservative loading and communality ranges.
Choose the primary estimator
Identify Pearson/PAF or polychoric/ordinal data risks.
Develop three scenarios
Favorable, baseline and unfavorable loadings, communalities and missingness.
Allow for losses
Account for invalid responses, missingness, failed attention checks and rare groups.
Reserve confirmation data
Choose sample splitting or separate validation collection.
Simulate where possible
Assess recovery under the intended structure and estimator.
Set stability criteria
Define loading, factor-congruence, membership and factor-count recovery targets.
Document decisions
Preserve assumptions and revise planning if pilot evidence differs.
9. Monte Carlo simulation tailored to the study
Simulation repeatedly generates data from the expected structure at different N values and measures correct factor-count, loading or membership recovery. This replaces a universal minimum with the N meeting the specific model’s criteria.
If simulation is unavailable, use literature-based scenarios and sensitivity analysis. Preacher and MacCallum (2003) emphasize that EFA requires justified decisions; software cannot replace design judgment.
| Component | Example specification | Outcome criterion |
|---|---|---|
| Model | 4 factors, 5 items per factor | Recovering 4 factors |
| Loadings | 0,45; 0,60; 0,75 | Loading bias |
| Communality | Low, moderate, high | Factor congruence |
| N | 150, 250, 350, 500 | Proportion meeting criteria |
| Data | Continuous or ordinal | Convergence and Heywood cases |
10. Check stability after data collection
Reaching the planned N does not establish stability. Bootstrap, repeated split-half or subsampling checks can reveal changes in factors, loadings and item membership. Watkins (2018) recommends documenting decisions and data characteristics so readers can assess EFA results.
Factor congruence or alignment helps compare solutions but requires consistent conventions and factor matching. A simple check tracks items that frequently switch factors or fall below substantively meaningful loadings.
11. Hypothetical example: planning recruitment for 30 items
These numbers are illustrative. A new scale has 30 items and five factors, six items each. A 90-person pilot yields loadings around 0.42 to 0.72, many communalities from 0.30 to 0.55, and 8% invalid responses. Weak items and four-category Likert data motivate the unfavorable scenario instead of a 10:1 ratio.
The team targets 320 usable EFA cases and 320 CFA cases, dividing by the expected completion rate of 0.92 to plan invitations. This is an illustrative design decision, not a universal standard. If resources allow only 350 overall, prioritize a full EFA study and later validation rather than two weak halves.
| Scenario | Assumptions | Decision |
|---|---|---|
| Favorable | Strong loadings, high communalities | N may be lower but validation remains necessary |
| Baseline | Moderate loadings, 6 items/factor | Retain the initial target |
| Unfavorable | Ordinal data, low communalities, 8% exclusions | Increase recruitment and monitor stability |
12. Eight sample-size justification mistakes
| Mistake | Problem | Correction |
|---|---|---|
| N = 200 is always sufficient | Ignores structure | Describe the model scenario |
| 10 respondents/item guarantees adequacy | An invariant ratio | Consider communality and overdetermination |
| High KMO proves sufficient N | KMO does not measure recovery | Assess stability |
| Large N repairs weak items | Precise estimation of a wrong model | Improve items and domain coverage |
| Splitting despite weak halves | Two underpowered analyses | Prioritize one objective or collect new data |
| Treating a small pilot estimate as certain | Large uncertainty | Use conservative ranges |
| Citing simulations outside their conditions | Limited applicability | Match loadings, factors and data type |
| No allowance for exclusions | Lower usable N | Plan losses beforehand |
13. APA 7 reporting template and checklist
Reporting example in English
EFA sample size was planned for [p] items and [k] factors, with [number] items per factor, expected loadings [range] and communalities [range]. Three scenarios were assessed for [Pearson/polychoric, estimator]. The [usable N] target increased to [recruitment N] for [rate] missing/invalid responses. [Simulation/literature-based sensitivity] indicated [criterion]. Final N was [ ]; stability was assessed using [bootstrap/subsampling/splitting/independent CFA].
- State item and factor counts.
- State items per factor.
- State expected loadings and communalities.
- Identify data and correlation types.
- Do not rely only on 5:1 or 10:1.
- Include an unfavorable scenario.
- Allow for missing and invalid data.
- Plan for subgroup analyses.
- Plan CFA or validation.
- Describe simulation if used.
- Prespecify recovery criteria.
- Check postcollection stability.
- Report Heywood cases and nonconvergence.
- Do not infer adequacy from KMO alone.
- Label illustrative numbers hypothetical.
Conclusion
EFA sample size belongs to a particular design, not the method’s name. Communalities, loadings, items per factor, complexity and data type jointly influence stability.
Good planning states assumptions, uses conservative scenarios, allows losses and reserves validation data. Stability still needs assessment after collection.
References
- DeVellis, R. F., & Thorpe, C. T. (2022). Scale development: Theory and applications (5th ed.). SAGE.https://us.sagepub.com/en-us/nam/scale-development/book269114
- de Winter, J. C. F., Dodou, D., & Wieringa, P. A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44(2), 147-181.https://doi.org/10.1080/00273170902794206
- MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4(1), 84-99.https://doi.org/10.1037/1082-989X.4.1.84
- Mundfrom, D. J., Shaw, D. G., & Ke, T. L. (2005). Minimum sample size recommendations for conducting factor analyses. International Journal of Testing, 5(2), 159-168.https://doi.org/10.1207/s15327574ijt0502_4
- Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift's electric factor analysis machine. Understanding Statistics, 2(1), 13-43.https://doi.org/10.1207/S15328031US0201_02
- Watkins, M. W. (2018). Exploratory factor analysis: A guide to best practice. Journal of Black Psychology, 44(3), 219-246.https://doi.org/10.1177/0095798418771807
- Worthington, R. L., & Whittaker, T. A. (2006). Scale development research: A content analysis and recommendations for best practices. The Counseling Psychologist, 34(6), 806-838.https://doi.org/10.1177/0011000006288127
Methodological note: Do not turn example values into universal cutoffs. Update the sample plan if loadings, communalities, factor count or item distributions differ from the assumptions.