Determining Sample Size for PLS-SEM and CB-SEM
There is no fixed minimum sample size for every SEM model. The sample must be adequate for the smallest important effect, measurement reliability, complexity, and missing-data rate.
The 10-times rule in PLS-SEM and N = 200 benchmark in CB-SEM are rough heuristics. Power analysis, inverse square root/gamma-exponential methods, or Monte Carlo simulation provide stronger justification for a specific model.
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 Can the Same Model Require Different Sample Sizes?
The required sample size increases when target effects are small, factor loadings are low, models contain many parameters, data are skewed or missing, or narrow confidence intervals are required. Wolf et al. (2013) show that SEM sample requirements vary substantially with loadings, the number of constructs, and model type.
A model that converges with a small N does not necessarily have sufficient power or low bias. Conversely, a large sample cannot correct misspecification, poor measurement, or biased sampling.
| Factor | When is a larger sample needed? |
|---|---|
| Effects | Small but important paths |
| Measurement | Low loadings, few indicators, low reliability |
| Model | Many parameters, mediation, groups, or interactions |
| Data | Missing data, unbalanced groups, nonnormality |
| Objective | Narrow CIs, stable prediction, invariance testing |
2. Limitations of the 10-Times Rule and the 200 Benchmark
The 10-times rule does not directly control power and may seriously underestimate requirements when effects are small. The inverse square root and gamma-exponential methods for PLS-SEM are better-founded options when their conditions of application hold (Kock & Hadaya, 2018). The 200 benchmark for CB-SEM likewise fails to reflect loadings, df, estimator type, and complexity.
A heuristic can provide an initial planning estimate, but proposals and articles should justify sample size using the minimum important effect and a quantitative procedure.
The effect size used in power analysis should come from theory, prior studies, or the smallest practically meaningful effect, rather than the sample that will itself be analyzed.
3. Choosing a Sample-Size Planning Method
| Method | Suitable for | Main inputs |
|---|---|---|
| Power analysis for regression/paths | Relatively simple PLS models | Number of predictors, α, power, effect size |
| Inverse square root or gamma-exponential | PLS-SEM based on the minimum path coefficient | Minimum path, α, power |
| Monte Carlo | CB-SEM, mediation, CFA, complex models | Loadings, paths, distributions, missing data |
| Precision planning | Objectives requiring narrow CIs | Desired CI width |
4. Planning Workflow
Finalize the model and main hypothesis
Identify the smallest important parameter to detect.
Choose α and power
State the Type I error rate and detection probability; a minimum power of 0,80 is conventional.
Specify simulation parameters
Use prior research or conservative scenarios for loadings, paths, and missing data.
Calculate the analysis N
Find the N meeting the target power, bias, coverage, and proportion of valid solutions.
Allow for attrition
Increase invitations according to expected nonresponse, exclusions, and missing data.
Document decisions in advance
Save code, assumptions, and sample-size results for transparent reporting.
5. Reporting Template
Example report
Sample size was planned for the primary parameter [ ], with a minimum effect of [ ], α = [ ], and power = [ ]. The [power/Monte Carlo] analysis assumed loadings [ ], missing data [ ], and estimator [ ], yielding a minimum analysis N of [ ]. After allowing for [ ]% attrition, the recruitment target was [ ]. The final sample N = [ ] met [criteria].
- Do not rely exclusively on the 10-times rule or 200 benchmark.
- State the minimum important effect size.
- Account for missing data and attrition.
- Plan separately for mediation, MGA, and interactions.
- Report the assumptions and sample-size calculation tools.
- Do not use post hoc results to rationalize N.
Conclusion
Sample-size planning is more than an administrative step before running software. It is a commitment that the design can answer the main question with adequate precision.
References
- Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. Educational and Psychological Measurement, 73(6), 913–934.https://doi.org/10.1177/0013164413495237
- Kock, N., & Hadaya, P. (2018). Minimum sample size estimation in PLS-SEM: The inverse square root and gamma-exponential methods. Information Systems Journal, 28(1), 227–261.https://doi.org/10.1111/isj.12131
Academic note: All illustrative values depend on assumptions. If the model changes after data collection, reassess power and precision rather than retaining the original justification.