Principal Component Analysis (PCA): How to Run It Online and Report It in APA7
Principal component analysis combines many correlated variables into a smaller number of uncorrelated components that capture as much of the variance as possible.
What is Principal Component Analysis (PCA)?
Principal component analysis combines many correlated variables into a smaller number of uncorrelated components that capture as much of the variance as possible.
When to use it
Use it to reduce the number of variables, to build summary scores, to remove multicollinearity before a regression, or to visualise high-dimensional data. It is a data-reduction method, not a model of latent causes.
Example question: Can my eight survey variables be summarised by two components?
Preparing your data
One row per participant and one numeric column per variable. Variables should be continuous or approximately so. Standardise variables measured on different scales (the correlation-matrix option does this).
Example dataset (simulated; first rows of 250): id, var1 to var8 (eight numeric variables).
| id | var1 | var2 | var3 | var4 | var5 | var6 | var7 | var8 |
|---|---|---|---|---|---|---|---|---|
| 1.0 | 9.04 | 10.69 | 8.92 | 9.01 | 10.91 | 9.93 | 11.55 | 10.78 |
| 2.0 | 10.85 | 10.73 | 13.15 | 12.61 | 8.6 | 7.28 | 9.01 | 7.65 |
| 3.0 | 7.35 | 7.46 | 7.79 | 7.82 | 9.37 | 9.14 | 10.07 | 8.54 |
| 4.0 | 11.95 | 12.3 | 12.98 | 12.79 | 11.0 | 9.47 | 8.15 | 10.37 |
| 5.0 | 10.05 | 10.08 | 9.81 | 10.18 | 10.57 | 8.97 | 10.92 | 10.96 |
| 6.0 | 8.78 | 8.41 | 9.2 | 9.14 | 10.84 | 10.17 | 9.74 | 10.15 |
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 Principal Component Analysis (PCA) 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 numeric variables. Choose how many components to keep and whether to rotate them (varimax is common).
- 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
- Variables are numeric and correlated; check KMO (about .60 or higher) and Bartlett's test.
- A sample of at least about 100–200 cases, or 5–10 cases per variable.
- Standardise variables with different units or use the correlation matrix.
- Choose the number of components using the scree plot, parallel analysis and interpretability.
- Check for outliers, which can distort components.
Key numbers to look at
- Eigenvalues and percentage of variance explained by each component.
- Scree plot to choose the number of components.
- Component loadings: correlations between variables and components.
- Component scores that can be used in later analyses.
Effect size
Report the variance explained by each retained component and the cumulative variance.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Principal Component Analysis (PCA) 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
- Reporting PCA as if it discovered latent factors; use EFA for that.
- Keeping components only by the eigenvalue-greater-than-1 rule.
- Mixing variables on different scales without standardising.
Related analyses and alternatives
- EFA: To model latent factors.
- CFA: To confirm a hypothesised structure.
- Heatmap: To inspect the correlation matrix first.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
How many components should I keep?
Combine several criteria: the scree plot, parallel analysis, the variance explained and whether the components are interpretable.
Do components have to be rotated?
No. Rotation, such as varimax, often makes loadings easier to interpret.
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.
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.