Exploratory Factor Analysis (EFA): How to Run It Online and Report It in APA7
Exploratory factor analysis uncovers the underlying latent factors that explain why a set of items are correlated, without specifying the structure in advance.
What is Exploratory Factor Analysis (EFA)?
Exploratory factor analysis uncovers the underlying latent factors that explain why a set of items are correlated, without specifying the structure in advance.
When to use it
Use it when developing a new scale or when the structure of an instrument is unknown, to decide how many factors there are and which items belong to which factor.
Example question: How many dimensions underlie my ten attitude items, and which items go together?
Preparing your data
One row per participant and one numeric column per item. All items should be measured on a similar scale.
Example dataset (simulated; first rows of 300): id, item1 to item9 (nine items from an imagined three-dimension scale).
| id | item1 | item2 | item3 | item4 | item5 | item6 | item7 | item8 | item9 |
|---|---|---|---|---|---|---|---|---|---|
| 1.0 | 4.85 | 3.59 | 4.6 | 3.81 | 4.09 | 5.64 | 3.79 | 2.69 | 2.94 |
| 2.0 | 5.05 | 3.02 | 5.04 | 3.61 | 4.42 | 6.26 | 4.9 | 3.08 | 4.42 |
| 3.0 | 5.34 | 5.32 | 3.7 | 2.61 | 2.87 | 3.39 | 1.47 | 3.69 | 3.85 |
| 4.0 | 5.12 | 3.81 | 5.49 | 4.28 | 3.95 | 5.83 | 4.95 | 4.69 | 3.46 |
| 5.0 | 3.86 | 4.02 | 6.6 | 5.44 | 4.53 | 4.94 | 5.6 | 5.54 | 5.58 |
| 6.0 | 4.1 | 5.18 | 5.85 | 4.63 | 5.23 | 4.07 | 2.73 | 3.09 | 2.19 |
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 Exploratory Factor Analysis (EFA) 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. Select the items. Choose the number of factors (guided by parallel analysis), the extraction method (for example maximum likelihood or principal axis) and the rotation (oblique, such as promax or oblimin, when factors are expected to correlate).
- 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
- Items correlate with one another (check the correlation matrix; many correlations above about .30).
- Sampling adequacy: Kaiser–Meyer–Olkin (KMO) of about .60 or higher, and a significant Bartlett's test of sphericity.
- Sample size of at least about 200, or 5–10 cases per item.
- Decide the number of factors using parallel analysis and the scree plot; the "eigenvalue greater than 1" rule often overestimates.
- Use an oblique rotation unless you have a strong reason to force uncorrelated factors.
Key numbers to look at
- KMO and Bartlett's test for suitability.
- Eigenvalues, scree plot and parallel analysis to choose the number of factors.
- Pattern loadings: items typically need a loading of about .40 or higher on one factor and low loadings on the others.
- Communalities and variance explained.
- Factor correlations when an oblique rotation is used.
Effect size
Factor loadings and the variance explained describe how well the factors summarise the items.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Exploratory Factor Analysis (EFA) in APA7 style
Template
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
- Using the eigenvalue greater than 1 rule as the only criterion.
- Running EFA on a very small sample.
- Interpreting factors without confirming them in a new sample with CFA.
Related analyses and alternatives
- CFA: To confirm the structure in another sample.
- PCA: For data reduction when no latent construct is assumed.
- Correlation: To inspect item correlations first.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What is the difference between EFA and PCA?
EFA models latent factors that cause the item correlations and separates common from unique variance. PCA simply forms weighted sums that capture as much total variance as possible.
Which rotation should I choose?
Choose an oblique rotation such as promax or oblimin when factors are expected to correlate, which is common in the social sciences.
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.
Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185. https://doi.org/10.1007/BF02289447
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.