The number of participants required for Confirmatory Factor Analysis (CFA) is not a single fixed value but rather depends on several critical factors, primarily the complexity of your model and the number of items within your scales. A widely accepted minimum guideline is to have at least 10 participants for each item included in your model.
Understanding CFA Sample Size Requirements
When planning a study using CFA, researchers often seek an exact number of participants, but the reality is more nuanced. While smaller samples might yield statistically significant results, they can be unstable and may not generalize well to the broader population. An adequate sample size is crucial for obtaining reliable parameter estimates, accurate model fit indices, and sufficient statistical power to detect true effects.
Key Factors Influencing Sample Size
Several considerations go beyond a simple head count of participants, shaping the ideal sample size for a robust CFA:
- Model Complexity: More complex models, featuring numerous latent factors, a high number of indicator items, inter-factor correlations, or specified cross-loadings, generally demand larger samples. Each additional parameter estimated increases the data requirement.
- Number of Items: As a foundational rule, a higher number of items in your scale or questionnaire necessitates more participants to ensure stable parameter estimates.
- Factor Loadings Strength: Items with strong factor loadings (i.e., highly related to their intended latent factor) can sometimes allow for slightly smaller samples, whereas weak loadings require more data to be reliably detected.
- Communality of Items: This refers to the proportion of variance an item shares with other items in its factor. High communalities can support smaller samples.
- Data Distribution: Non-normal data often requires larger samples, especially when using estimation methods sensitive to distributional assumptions (like Maximum Likelihood).
- Estimation Method: Different estimation methods (e.g., Maximum Likelihood, Weighted Least Squares Mean and Variance adjusted – WLSMV) have varying sensitivities to sample size and data characteristics. Robust estimators might be more forgiving with non-normal data but don't eliminate the need for sufficient participants.
- Desired Statistical Power: To detect a true effect (e.g., a specific factor loading or factor correlation) with a high probability, researchers often conduct a power analysis, which can indicate the required sample size for a given effect size, alpha level, and desired power.
- Missing Data: The presence of missing data can effectively reduce your sample size, meaning you might need to recruit more participants initially to account for potential attrition or incomplete responses.
General Guidelines and Rules of Thumb
While no "one size fits all" answer exists, several widely adopted guidelines can help researchers determine an appropriate sample size for CFA:
- Participants per Item Rule: As a minimum, aim for at least 10 participants for each item in your Confirmatory Factor Analysis model. For instance, a scale with 20 items would ideally require at least 200 participants (20 items * 10 participants/item). Many researchers advocate for an even higher ratio, such as 15 or 20 participants per item, especially for more complex models or when expecting smaller effects.
- Absolute Minimums: Some statistical experts suggest absolute minimum sample sizes, often citing 100 to 200 participants as a general threshold for basic CFA models, even if the item count might suggest slightly fewer. Samples below 100 are generally discouraged.
- N:p Ratio (Participants to Parameters Ratio): This guideline considers the ratio of the number of participants (N) to the number of estimated parameters (p) in the model. Ratios ranging from 5:1 to 20:1 are commonly recommended. A 10:1 ratio is often considered a good balance, meaning you should have 10 participants for every parameter your model estimates. Complex models or those with weak effects may require a higher ratio (e.g., 20:1).
The following table summarizes these common recommendations:
| Guideline Category | Specific Recommendation | Description |
|---|---|---|
| Participants per Item | At least 10 participants per item | A widely used minimum. More (15-20) is often preferred, especially for intricate models or when aiming for higher precision. |
| Absolute Minimum | 100-200 participants | A baseline for simple CFA models, regardless of the number of items. Lower numbers risk unstable results. |
| N:p Ratio | 5:1 to 20:1 (Participants: Estimated Parameters) | Considers model complexity by relating sample size to the number of statistical values the model needs to determine. A 10:1 ratio is a common target. |
| Model Complexity | Larger samples for more complex models | Models with many factors, indicators, or inter-factor relationships inherently demand more data to achieve stable and reliable estimates. |
| Statistical Power | Varies based on desired power and effect size | For detecting smaller effects or achieving high confidence in your findings, a formal power analysis is recommended, which often indicates a larger sample size requirement. |
Example:
Imagine you are conducting a CFA for a construct measured by 15 items, designed to load onto three distinct factors.
- Using the "10 participants per item" rule: You would need at least 15 items * 10 participants/item = 150 participants.
- Considering the "N:p Ratio": If your model estimates, for example, 30 parameters (factor loadings, error variances, factor covariances), then a 10:1 ratio would suggest 30 * 10 = 300 participants.
As this example illustrates, the number can vary, and it's always safer to err on the side of a larger sample, especially if you anticipate a more complex model or subtle effects.
Practical Considerations for Researchers
- Power Analysis: For the most rigorous approach, conduct a power analysis specific to your CFA model. Specialized software or online calculators can help estimate the required sample size based on your hypothesized model, expected effect sizes, and desired statistical power.
- Pilot Testing: A pilot study with a small sample can help identify potential issues with your scale items and provide preliminary data to refine your sample size estimation.
- Reporting: Clearly report your rationale for the chosen sample size in your methodology section, referencing relevant guidelines or power analysis results.
The Importance of Adequate Sample Size
An insufficient sample size can lead to several problems in CFA, including:
- Unstable Parameter Estimates: Loadings and covariances may fluctuate wildly across different samples, making results unreliable.
- Inaccurate Model Fit Indices: Fit indices (e.g., CFI, TLI, RMSEA) can be biased with small samples, potentially leading to incorrect conclusions about how well your model fits the data.
- Lack of Statistical Power: You might fail to detect genuine relationships or effects, leading to Type II errors.
- Poor Generalizability: Results from small samples are less likely to represent the true population, limiting the external validity of your findings.
Therefore, while there isn't a single "exact" number, researchers should carefully consider their model's specifics and aim for a sample size that provides robust and trustworthy results.
