Exploratory factor analysis (EFA) is a multivariate statistical technique used to identify the underlying latent structure of a set of observed variables. It is applied when the researcher does not have a predefined theory about how variables should group together. Instead of testing a model, EFA explores patterns in the data to determine how many factors exist and which variables load onto each factor.
When researchers ask what is exploratory factor analysis, the most accurate answer is that EFA is a data-reduction and structure-detection method. It simplifies large sets of variables into fewer interpretable dimensions while retaining as much shared variance as possible.
Exploratory factor analysis is widely used in survey research, psychology, education, health sciences, and social sciences, particularly during early instrument development or when adapting existing scales to new populations.
What Exploratory Factor Analysis Can Be Used To Do
Exploratory factor analysis can be used to:
- Identify latent constructs underlying survey items
- Reduce large questionnaires into interpretable dimensions
- Detect poorly performing or redundant items
- Inform scale refinement before confirmatory factor analysis
- Support construct validity during instrument development
In applied research, EFA is often the first step before confirmatory factor analysis or structural equation modeling. Using EFA correctly helps prevent model misspecification and weak measurement models later in the analysis process.
Sample Size for Exploratory Factor Analysis
Determining the appropriate sample size for exploratory factor analysis is critical for stable and interpretable results. There is no single rule, but several well-established guidelines exist.
Common recommendations include:
- A minimum of 5 to 10 participants per variable
- An absolute minimum sample size of 150 to 300 cases
- Larger samples for weaker communalities or complex models
More important than raw sample size is factorability. High communalities, strong factor loadings, and clear structure can compensate for smaller samples, whereas weak data require substantially larger samples.
Researchers should always assess sampling adequacy using the Kaiser–Meyer–Olkin (KMO) statistic and Bartlett’s test of sphericity before proceeding.
Exploratory Factor Analysis Assumptions
Before running EFA, several assumptions should be evaluated:
- Variables should be at least ordinal, preferably continuous
- Adequate correlations must exist among variables
- Multicollinearity should not be excessive
- Sampling adequacy must be sufficient (KMO > 0.60)
Although normality is less strict for EFA than for confirmatory methods, extreme skewness or outliers can distort factor extraction. Addressing these issues prior to analysis improves the quality and interpretability of results.
Understanding exploratory factor analysis assumptions helps prevent misinterpretation and reviewer criticism.
How to Do Exploratory Factor Analysis in SPSS
SPSS provides a dedicated factor analysis procedure that allows researchers to conduct EFA without additional software.
How to Do Exploratory Factor Analysis in SPSS: Step-by-Step
- Prepare the data
Screen for missing values, outliers, and coding errors. - Check factorability
Run KMO and Bartlett’s test to confirm suitability. - Choose extraction method
Principal axis factoring is preferred for latent constructs, while principal components analysis is used for data reduction. - Determine number of factors
Use eigenvalues, scree plot, and theoretical justification. - Select rotation method
Use oblique rotation when factors are correlated and orthogonal rotation when they are assumed independent. - Interpret factor loadings
Retain items with strong loadings and minimal cross-loadings.
This process directly addresses how to do exploratory factor analysis in SPSS in a defensible and publication-ready manner.
Exploratory Factor Analysis SPSS Interpretation
Correct exploratory factor analysis SPSS interpretation requires examining several outputs simultaneously rather than relying on a single statistic.
Communalities
Communalities indicate how much variance in each variable is explained by the extracted factors. Values above 0.40 are generally acceptable.
Factor Loadings
Loadings represent the strength of the relationship between a variable and a factor. Loadings above 0.50 are preferred, though thresholds depend on sample size.
Cross-Loadings
Items loading strongly on multiple factors may lack conceptual clarity and are often candidates for removal.
Total Variance Explained
The cumulative variance explained by retained factors should be theoretically meaningful and sufficient for the research context.
Interpretation must always align statistical results with substantive theory.
Exploratory Factor Analysis in R vs SPSS
While this guide focuses on SPSS, many researchers also consider exploratory factor analysis in R. R offers greater flexibility, advanced estimation methods, and reproducible workflows. However, it requires coding proficiency and careful package selection.
SPSS remains popular for applied research due to its graphical interface, standardized output, and accessibility for non-programmers. The choice between SPSS and R should be driven by researcher expertise, institutional requirements, and publication expectations.
Example of Exploratory Factor Analysis
To demonstrate exploratory factor analysis in practice, a 15-item student learning experience questionnaire was analyzed using exploratory factor analysis in SPSS. The items were designed to measure underlying dimensions of learning behavior, motivation, and self-regulation, although the exact factor structure had not been previously validated.
The analysis followed recommended EFA procedures, beginning with assessment of factorability, followed by factor extraction, rotation, and interpretation.
Assessment of Factorability
Prior to extraction, sampling adequacy and correlation structure were evaluated. The Kaiser–Meyer–Olkin (KMO) measure indicated adequate sampling adequacy, and Bartlett’s test of sphericity was statistically significant, confirming that the data were suitable for exploratory factor analysis.
| Test | Value | Interpretation |
|---|---|---|
| KMO Measure | 0.84 | Adequate |
| Bartlett’s Test χ² | 1246.31 | Significant |
| df | 105 | — |
| p-value | < .001 | Factorable |
These results indicate that sufficient shared variance existed among items to justify factor extraction.
Factor Extraction and Rotation
Principal axis factoring was used as the extraction method because the goal was to identify latent constructs rather than reduce data. The number of factors was determined using a combination of eigenvalues, scree plot inspection, and theoretical interpretability.
Three factors with eigenvalues greater than one were retained. An oblique rotation (Promax) was applied because the underlying constructs were expected to be correlated.
Rotated Factor Loadings
The rotated factor matrix showed a clear three-factor solution. Items with loadings below 0.40 or with substantial cross-loadings were excluded from interpretation.
| Item | Factor 1 (Learning Behavior) | Factor 2 (Motivation) | Factor 3 (Self-Regulation) |
|---|---|---|---|
| LB1 | 0.74 | — | — |
| LB2 | 0.69 | — | — |
| LB3 | 0.72 | — | — |
| LB4 | 0.66 | — | — |
| M1 | — | 0.71 | — |
| M2 | — | 0.75 | — |
| M3 | — | 0.68 | — |
| M4 | — | 0.73 | — |
| SR1 | — | — | 0.77 |
| SR2 | — | — | 0.70 |
| SR3 | — | — | 0.74 |
| SR4 | — | — | 0.69 |
Note. Loadings below 0.40 are suppressed for clarity.
All retained items loaded strongly on a single factor, with no problematic cross-loadings, supporting a clean and interpretable factor structure.
Variance Explained
The three-factor solution explained a substantial proportion of total variance.
| Factor | Eigenvalue | % Variance Explained | Cumulative % |
|---|---|---|---|
| Factor 1 | 4.12 | 27.5% | 27.5% |
| Factor 2 | 2.83 | 18.9% | 46.4% |
| Factor 3 | 2.14 | 14.3% | 60.7% |
The cumulative variance explained exceeded 60 percent, which is generally acceptable in social science research.
APA-Style Reporting of EFA Results
An exploratory factor analysis was conducted using principal axis factoring with Promax rotation to examine the underlying structure of the 15-item learning experience scale. The Kaiser–Meyer–Olkin measure verified sampling adequacy (KMO = .84), and Bartlett’s test of sphericity was significant, χ²(105) = 1246.31, p < .001, indicating suitability for factor analysis. Three factors were retained based on eigenvalues greater than one and scree plot inspection. The rotated solution revealed a clear three-factor structure corresponding to learning behavior, motivation, and self-regulation, explaining 60.7% of the total variance. All retained items demonstrated substantial factor loadings (≥ .66) on their respective factors with no significant cross-loadings, supporting the interpretability of the solution.
Common Mistakes in Exploratory Factor Analysis
Frequent errors include:
- Using principal components analysis when latent constructs are intended
- Retaining factors based solely on eigenvalues greater than one
- Ignoring theoretical justification
- Failing to report rotation method
- Overinterpreting weak or unstable factors
Avoiding these mistakes improves credibility and reduces revision requests.
Conclusion
Exploratory factor analysis in SPSS is a powerful technique for uncovering latent structure and refining measurement instruments. When applied correctly, EFA supports construct validity, improves scale quality, and lays the foundation for confirmatory factor analysis and advanced modeling.
Understanding what exploratory factor analysis is, knowing how to do exploratory factor analysis in SPSS, meeting sample size and assumption requirements, and applying correct interpretation standards are essential for defensible research outcomes.
For researchers working on theses, dissertations, or journal submissions, errors in EFA often lead to rejection or major revisions. Having the analysis conducted and interpreted correctly from the start saves time and protects research credibility.
