Confirmatory Factor Analysis (CFA): How to Run It Online and Report It in APA7
Confirmatory factor analysis tests whether a set of items measures the latent factors you expect, based on a structure you specify in advance.
What is Confirmatory Factor Analysis (CFA)?
Confirmatory factor analysis tests whether a set of items measures the latent factors you expect, based on a structure you specify in advance.
When to use it
Use it to validate a questionnaire or scale with a known structure, to test whether items load on the factors they were designed for, and to check reliability and discriminant validity before using the scales in further analyses.
Example question: Do the nine items form the three factors the scale authors proposed?
Preparing your data
One row per participant, one numeric column per item, with clear item names. Reverse-score items before the analysis where needed.
Example dataset (simulated; first rows of 300): id, a1 to a3, b1 to b3, c1 to c3 (nine items for three factors).
| id | a1 | a2 | a3 | b1 | b2 | b3 | c1 | c2 | c3 |
|---|---|---|---|---|---|---|---|---|---|
| 1.0 | 4.16 | 3.96 | 4.5 | 4.5 | 3.71 | 2.82 | 4.17 | 2.54 | 4.17 |
| 2.0 | 2.62 | 2.53 | 2.51 | 2.54 | 2.45 | 3.22 | 4.01 | 2.57 | 2.52 |
| 3.0 | 3.2 | 3.19 | 2.56 | 2.45 | 2.67 | 2.91 | 4.08 | 2.24 | 2.92 |
| 4.0 | 4.31 | 3.65 | 3.35 | 2.53 | 4.74 | 3.62 | 4.63 | 5.19 | 3.04 |
| 5.0 | 2.66 | 2.43 | 2.43 | 2.66 | 3.44 | 5.66 | 4.85 | 5.08 | 5.5 |
| 6.0 | 4.1 | 4.1 | 3.71 | 3.07 | 5.4 | 5.05 | 5.7 | 4.03 | 5.71 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Confirmatory Factor Analysis (CFA) tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Assign each item to a factor and decide whether factors may correlate (usually yes). Choose an estimator that matches the item scale (robust or ordinal estimators for Likert items with few categories).
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- The factor structure is specified before looking at the data, from theory or an earlier study.
- Each factor has at least three indicators; the model must be identified.
- A large enough sample (at least 200, or several cases per item).
- Items are continuous or treated as ordinal with an appropriate estimator.
- Do not split one sample into exploratory and confirmatory halves unless it is large; better to validate on a new sample.
Key numbers to look at
- Fit indices: χ²(df), CFI, TLI, RMSEA with 90% CI, SRMR.
- Standardised loadings: values of about .50–.70 or higher indicate good indicators.
- Factor correlations: very high values (above about .85) suggest the factors may not be distinct.
- Reliability: composite reliability and Cronbach's α or McDonald's ω, about .70 or higher.
- Average variance extracted (AVE): above .50 supports convergent validity.
Effect size
Standardised factor loadings and factor correlations describe the strength of the measurement model.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Confirmatory Factor Analysis (CFA) in APA7 style
Template
Present loadings in an APA table.
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Treating CFA as exploratory by repeatedly modifying the model.
- Reporting a factor structure without reliability.
- Ignoring that Likert items with five or fewer categories may need an ordinal estimator.
Related analyses and alternatives
- EFA: If you do not know the structure yet.
- SEM: To add structural paths between factors.
- PCA: To reduce items to components without a latent-variable model.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What is the difference between CFA and EFA?
EFA lets the data suggest the factor structure. CFA tests a structure you specify before analysing the data.
How many items per factor do I need?
At least three for a stable, identified factor; four to six is better.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50. https://doi.org/10.1177/002224378101800104
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.