METHOD GUIDE
Exploratory Factor Analysis in SPSS
Extraction, Retention and Rotation
EFA in SPSS starts from several defaults in the Factor dialog that are not the choices most studies need. Extraction method, number of factors and rotation are each set on purpose, then traced through Total Variance Explained and the pattern loadings into the write-up.
IN SHORT
What the Factor Procedure Estimates and What Stays Your Decision
A factor analysis explores how many underlying dimensions account for the correlations among a set of items, and which items belong to each. It suits questionnaire or test items measured on ordered response scales, in a sample large enough for stable correlations, and the number of factors is a judgment, not an output. To run EFA in SPSS, open Analyze, Dimension Reduction, Factor, enter the items, request KMO and Bartlett’s test under Descriptives, choose the extraction method and the rule for the number of factors, and select a rotation (labels vary by version). OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
Retained factors usually become scales, and Reliability Analysis (Cronbach's Alpha) covers how well each of those scales holds together afterward.
Exploratory Factor Analysis (EFA)
The factor model fitted within your study design, with the suitability checks, the retention decision, the rotation and the loadings table agreed for your items and sample.
Principal Component Analysis (PCA)
Component scores for reducing many variables to a few composites, for when the aim is a summary of the data and not a model of latent dimensions.
BEFORE YOU RUN IT
Readiness of the Items for Factoring
Whether the items suit factoring at all, and on which correlations, is settled in the data and not by an output.
Items and Response Format Items with five or more ordered categories and a reasonable spread behave well with Pearson correlations. Few categories or strong skew can produce artificial factors, and a polychoric-based approach is considered.
Sample and Correlations No single ratio of cases to items settles the sample size. Stable results depend on the communalities, the items per factor and the strength of the correlations, so a small sample is a stated limitation.
Aim of the Analysis Exploring structure calls for common-factor extraction, while summarizing items into scores can use components. The SPSS default is a component method, so the extraction is chosen on purpose and named.
A Plan for Validation Fitting a confirmatory model to the data that suggested the structure inflates its fit. A separate sample, or a split planned beforehand, is used to test what the exploratory step found.
IN SPSS
How to Run EFA in SPSS
Every choice below is a setting in the Factor dialog of IBM SPSS, and three of its defaults are changed on purpose. Labels can vary by version.
- Inspect the items for missing values, reversed wording and the correlation matrix before extracting anything.
- Choose Analyze, Dimension Reduction, Factor and move the items into the Variables box.
- Under Descriptives, tick KMO and Bartlett’s test of sphericity.
- Under Extraction, replace the default Principal components with Principal axis factoring or Maximum likelihood, and tick Scree plot.
- Under Extract, replace the eigenvalue-above-1 default with a fixed number of factors chosen from the evidence.
- Under Rotation choose Direct Oblimin or Promax, or Varimax if uncorrelated factors are intended, and sort the loadings by size under Options.
READING THE OUTPUT
Which Factor Tables Carry the Retention and Rotation Evidence
SPSS prints Total Variance Explained, a scree plot and a loadings matrix for each rotation, and the decision to keep a factor rests on several of them together.
| Output element | What it tells you | What to check |
|---|---|---|
| KMO and Bartlett’s Test | The Kaiser-Meyer-Olkin Measure of Sampling Adequacy and Bartlett’s Test of Sphericity | That KMO is read as a screen, with values below about .50 a warning, and that a significant Bartlett test is expected in most samples and does not confirm suitability |
| Communalities | The Initial and Extraction share of each item’s variance accounted for by the retained factors | That low values flag items that do not fit, and an extraction value above 1 signals a problem in the solution |
| Total Variance Explained | Eigenvalues, percent of variance and cumulative percent for the initial, extraction and rotation sums | That the count of eigenvalues above 1 is one input to retention, and that rotation sums after an oblique rotation cannot be added |
| Scree Plot | The eigenvalues plotted against the factor number | That the bend is read with other evidence and the judgment is stated, since the elbow is not always clear |
| Factor Matrix (unrotated) | Each item’s loading on each factor before rotation | That it is treated as a stage, because the first factor tends to load on almost every item |
| Rotated Factor Matrix or Pattern Matrix | The loadings after Varimax, or after an oblique rotation for the Pattern Matrix | That items with cross-loadings or no clear loading are flagged, and the cutoff was set beforehand |
| Structure Matrix and Factor Correlation Matrix | The item-factor correlations and the correlations among factors, for oblique rotation only | That the factor correlations show whether oblique rotation was needed |
| Reproduced Correlations (if requested) | The correlations implied by the model and the residuals against the observed ones | That few nonredundant residuals exceed 0.05 in absolute value |
REPORTING
Reporting the Extraction, the Rotation and the Retained Factors
The methods paragraph names every choice made in the Factor dialog, and the loadings table carries the result.
Name the extraction method, the rotation and the correlation matrix analyzed, then give the sample size, KMO = ___ and Bartlett’s χ²(df = ___) = ___, p = ___. State the retention rule with the evidence behind it, the variance accounted for by the retained factors where it applies, and how many items were removed and why. Present a table of pattern loadings and communalities, with the factor correlations for an oblique rotation, and hide loadings below the cutoff stated in advance. The Factor procedure prints no standard errors or intervals for loadings, so stability is shown by repeating the solution in a split or a second sample. Describe factors as dimensions that account for the item correlations, name them only after reading the items that load, and avoid presenting them as proof that a construct exists.
COMMON MISTAKES
Decisions in the Factor Dialog That Quietly Shape the Result
Several defaults produce a solution without any warning, so the problems below show only when the choices behind the output are examined.
Components Reported as Factors The default extraction in the Factor dialog analyzes total variance, not shared variance. Calling the result a factor analysis without saying which method ran misstates what was estimated.
Eigenvalue Rule as the Verdict Keeping every factor with an eigenvalue above 1 tends to overstate the number of factors, especially with many items. The scree plot, interpretability and a comparison with eigenvalues from random data are weighed with it.
Varimax by Habit Orthogonal rotation forces the factors to be uncorrelated, which is rarely true of psychological or social constructs. An oblique rotation is run first, and Varimax is kept only if the factors prove nearly uncorrelated.
Items Dropped by Loading Alone Removing items in repeated rounds until the loadings look clean fits the solution to the sample. The rules for deletion are set beforehand and every removed item is reported.
A Cutoff Without Context A loading of .40 is not a law. Its meaning depends on the sample size, cross-loadings and the item content, so the cutoff and any exceptions are stated and justified.
Same Data Used to Confirm A confirmatory model tested on the sample that produced the factors looks better than it deserves. The structure found here is tested on separate data.
Solution already extracted? Independent Statistical Review checks the extraction method, the retention decision and the loadings table before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About Factor Output in SPSS
Rotation comes first here, since it changes every loading that follows, then the KMO screen and the matrix to report after an oblique solution.
How do I choose the SPSS factor rotation: Varimax, Direct Oblimin or Promax?
Start with an oblique rotation such as Direct Oblimin or Promax, and keep Varimax only if the factor correlations turn out to be close to zero. Varimax forces the factors to be uncorrelated, which can distort the loadings when the constructs overlap, while an oblique rotation lets the data show the correlation and reduces to a similar result if there is none. The choice is made before looking at which solution is easiest to interpret.
What should the KMO and Bartlett's test in SPSS show before I continue?
They screen the correlation matrix for suitability, and neither settles the question alone. The overall KMO value, with item-level values on the diagonal of the anti-image correlation matrix when requested, flags items that share too little variance with the rest, and values below about .50 are a warning. Bartlett’s test only rejects a matrix of zero correlations, which most real samples do, so a significant result is expected and uninformative on its own.
Which matrix do I read after an oblique rotation, Pattern or Structure?
Read the Pattern Matrix, which shows each factor’s unique contribution to an item, and use the Structure Matrix and the Factor Correlation Matrix as support. Structure coefficients are correlations that include the part shared through correlated factors, so every item can look related to every factor. Report the pattern loadings, the factor correlations and the communalities together so that readers can rebuild the picture.
Can OnlineSPSS review the extraction and rotation in my factor solution?
Yes. An in-house PhD-level statistician can review the method, the retention decision and the rotation against your items and sample, or carry out the analysis on your data from the start. For a finished solution, Results Reporting & Interpretation handles the loadings table and the methods paragraph. The naming of factors and the conclusions remain yours.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
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NEXT STEP
How Many Factors
Can Your Items Support?
Attach the item wording, the sample size and the factor output you have. A Research Coordinator reviews them, and the extraction, retention and rotation work is set out in the confirmed scope.
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