How to Report Exploratory Factor Analysis in APA 7 (With Example)

Exploratory factor analysis (EFA) identifies the underlying structure in a set of observed variables: it tells you how many meaningful groups of items exist and which items belong together. The APA 7 write-up requires statistics at three levels: adequacy of the correlation matrix (KMO and Bartlett's test), decisions about extraction and retention based on the unreduced correlation matrix, and the final factor solution with communalities and loadings. Use principal axis factoring (PAF) or maximum likelihood extraction for EFA; principal components analysis (PCA) is different and should not be called factor analysis.

What you need before you write a single word

An APA 7 write-up of EFA needs three sections of statistics.

Correlation matrix adequacy:

1. Kaiser-Meyer-Olkin (KMO) measure overall (and per-item, if checking adequacy for each variable).
2. Bartlett's test of sphericity (χ², degrees of freedom, p value).

Extraction decision:

1. The extraction method (principal axis factoring, maximum likelihood; not principal components analysis).
2. A retention criterion based on eigenvalues of the unreduced correlation matrix: Kaiser criterion (eigenvalue > 1), parallel analysis, scree plot interpretation, or theory.
3. The number of factors retained.

Factor solution:

1. The rotation method (varimax, oblimin, promax, or none). Orthogonal rotations (e.g., varimax) give a Rotated Factor Matrix; oblique rotations give a Pattern Matrix and Structure Matrix.
2. The factor loadings for each item and factor (usually in a table).
3. Extraction communalities (variance in each item explained by the extracted factors). Initial communalities (SMC) are not reported.
4. Variance explained by the rotated solution overall and per factor.
5. Cronbach's alpha for each factor (subscale), computed from your sample.

The APA 7 format template

Start with the adequacy test, then the extraction reasoning, then the solution:

The suitability of the data for factor analysis was assessed using the Kaiser-Meyer-Olkin measure and Bartlett's test of sphericity. The KMO measure was [X] (Kaiser, 1974), and Bartlett's test was statistically significant, χ²([df]) = [X], p < .001, indicating that the correlation matrix differed significantly from an identity matrix. An exploratory factor analysis was conducted on the [N] cases with [p] items using principal axis factoring (converged in [k] iterations) with varimax rotation (Kaiser normalization). Based on eigenvalues of the unreduced correlation matrix, parallel analysis suggested [n] factors (95th percentile eigenvalues: [list]). The final solution extracted [n] factors, accounting for [X]% of the total variance (rotation sums of squared loadings). Items were considered to load on a factor if the loading was ≥ .30 in absolute value; a factor's sign is arbitrary.

Formatting rules reviewers actually check:

• No leading zero on p, KMO, loadings, and alpha; keep leading zero on everything else.
• Report both adequacy tests before the final solution.
• State the extraction method (PAF or maximum likelihood), rotation method (e.g., varimax with Kaiser normalization), and sample size explicitly.
• Say what criterion you used to decide how many factors, using eigenvalues from the unreduced correlation matrix (SPSS's "Initial Eigenvalues" column).
• Variance explained is expressed as percentage of total variance (rotation sums / number of items × 100), not as a percentage that adds beyond the total extracted variance.
• Loadings below .30 should not appear in the table, or appear as blank cells.
• Report extraction communalities (from the reduced matrix after PAF), not initial communalities.
• Round loadings and communalities to two or three decimals. Round variance percentages to one or two decimals (SPSS prints two).
• Italic statistics and N for sample size.
• "Note." in the table note (not "Note:").

A worked example

Suppose 247 employees completed a 12-item work satisfaction questionnaire (five-point Likert scale, 1 = strongly disagree to 5 = strongly agree). The items measure three underlying constructs: autonomy, workload, and decision-making influence.

Adequacy test results:

• KMO = .80 (meritorious).
• Bartlett's χ²(66) = 1317.12, p < .001 (matrix not an identity).

Extraction reasoning:

• Method: principal axis factoring (PAF); communalities converged (largest change < .001) in 11 iterations, maximum 25.
• Retention criterion: eigenvalues of the unreduced correlation matrix, using the Kaiser criterion (eigenvalue > 1) and parallel analysis (95th percentile: 1.45, 1.34, 1.25).
• Eigenvalues: 3.22, 2.97, 2.02 (each above 1 and above its parallel-analysis threshold). The fourth eigenvalue (0.85) is below 1 and below its threshold (about 1.18), so three factors are retained.
• Rotation: varimax with Kaiser normalization.

Item decisions:

• Item 12 was retained because its loading (.36) met the ≥ .30 threshold, but it is the weakest item. Cronbach's alpha for Factor 1 is .85 with Item 12 and .89 without; the item slightly reduces internal consistency.

Final solution:

• 3 factors extracted via PAF, accounting for 58.8% of the total variance (23.6%, 21.2%, 14.0% respectively).

Written up in APA 7:

The adequacy of the correlation matrix for factor analysis was assessed using the Kaiser-Meyer-Olkin measure and Bartlett's test of sphericity. The KMO measure was .80, indicating meritorious sampling adequacy (Kaiser, 1974), and Bartlett's test was statistically significant, χ²(66) = 1317.12, p < .001. An exploratory factor analysis was conducted on 247 employees' responses to a 12-item work satisfaction scale using principal axis factoring (converged in 11 iterations) with varimax rotation (Kaiser normalization). Based on eigenvalues of the unreduced correlation matrix, parallel analysis (95th percentile eigenvalues: 1.45, 1.34, 1.25) suggested three factors with eigenvalues of 3.22, 2.97, and 2.02. The final solution extracted three factors, accounting for 58.8% of the total variance (rotation sums of squared loadings). Items were retained if they loaded ≥ .30 in absolute value. Item 12 met this threshold (loading = .36) but is the weakest item; Cronbach's alpha for Factor 1 was .85 with Item 12 and .89 without. Cronbach's alpha values for the three factors were .85, .87, and .78, indicating good internal consistency. A factor's sign is arbitrary; here, positive loadings indicate higher perceived control, more manageable workload, and greater decision influence, respectively.

The APA 7 factor analysis table

The loadings table is the centerpiece. APA tables use horizontal rules only. Report extraction communalities, not initial communalities.

Note. N = 247. EFA with principal axis factoring (communalities converged in 11 iterations, criterion .001) and varimax rotation (Kaiser normalization). Loadings < |.30| are suppressed. h² = extraction communality. Item 12 is the weakest item (lowest communality, smallest loading). Factors are reflected so primary loadings are positive.

Total Variance Explained table (SPSS format)

For a complete report, show Initial Eigenvalues (from the unreduced correlation matrix, for the retention decision), Extraction Sums (from the reduced matrix after PAF), and Rotation Sums (after varimax). Rotation sums differ per factor but the total variance is preserved.

Note. The initial eigenvalues are from the unreduced correlation matrix and are used for the retention decision (Kaiser criterion, parallel analysis, scree plot). The extraction sums show what PAF extracted. The rotation sums show the variance redistribution after varimax rotation; the total variance (58.84%) is preserved.

Where to find these numbers in SPSS

Analyze > Dimension Reduction > Factor:

• KMO and Bartlett's Test: Kaiser-Meyer-Olkin Measure; Bartlett's Approx. Chi-Square, df, and Sig.
• Communalities: report the "Extraction" column (communalities after PAF). Do not report "Initial" (SMC communalities).
• Total Variance Explained: the three-part table with Initial Eigenvalues (for retention decisions), Extraction Sums of Squared Loadings, and Rotation Sums of Squared Loadings.
• Rotated Factor Matrix: the loadings after rotation (this name applies to orthogonal rotations like varimax; oblique rotations produce Pattern Matrix and Structure Matrix). SPSS can suppress small loadings if you tick "Suppress absolute values less than [threshold]" (commonly .30 or .40).
• Factor Score Coefficient Matrix (if needed): shows the regression weights for scoring individuals on each factor (not the loadings themselves).

In the dialog, choose:

• Extraction: Principal Axis Factoring (for EFA of latent constructs). Do NOT use Principal Components unless you are doing PCA data reduction.
• Number of factors: Fixed (specify based on parallel analysis, scree plot, or theory). Do NOT tick "Eigenvalues greater than 1" if you want to run parallel analysis.
• Rotation: Varimax (orthogonal, produces Rotated Factor Matrix); Oblimin or Promax (oblique, produce Pattern and Structure matrices).

Mistakes reviewers catch

• Using PCA instead of PAF for factor analysis. Principal components analysis summarizes observed variables; exploratory factor analysis assumes latent common factors. Use PAF, maximum likelihood, or alpha factoring. Do not call PCA "factor analysis."
• Using eigenvalues from the reduced correlation matrix for the retention decision. Retention (Kaiser criterion, parallel analysis, scree plot) must be based on eigenvalues from the unreduced correlation matrix (SPSS's "Initial Eigenvalues"). Extraction eigenvalues are for a different purpose.
• Retaining factors by eigenvalue > 1 alone. This is a rule of thumb, not a law. Use parallel analysis (95th percentile of random eigenvalues), inspect the scree plot, and consider theory.
• Not stating the rotation method or calling all rotations "varimax." Orthogonal (Varimax) and oblique (Oblimin, Promax) rotations give different results and have different interpretations. State the method and normalization (e.g., "varimax with Kaiser normalization").
• Reporting initial communalities (SMC). Report extraction communalities only (from the reduced matrix after PAF).
• Ignoring cross-loadings or low communalities. If an item loads substantially on multiple factors or has low communality, discuss it. Low communality often indicates an ambiguous or off-topic item.
• Expressing variance as "percentage of extracted variance" or implying it adds to 100%. After rotation, each factor's variance is expressed as percentage of total variance (sum of squared loadings / number of items × 100). The rotation sums total equals the extraction sums total (preserves total extracted variance) but is redistributed among factors.
• Missing Cronbach's alpha per subscale. Once you have factors, compute alpha from your sample for each factor (and consider whether weak items should be removed).
• Assuming a factor's sign has meaning. A factor's sign is arbitrary (you can flip all loadings on a column by multiplying by −1 without changing the analysis). Report the sign you used, but do not interpret a negative sign as "lower" or "worse."

Before you report: did you choose the right number of factors?

Use eigenvalues of the unreduced correlation matrix (not extraction eigenvalues). Three methods guide the decision.

Eigenvalue rule (Kaiser criterion): retain factors with eigenvalue > 1. It is simple and standard but often over-extracts with fewer than 20 variables.

Scree plot: plot eigenvalues in descending order and look for an "elbow", a drop-off where the line flattens. Factors above the elbow are usually retained. Your interpretation is subjective but guided by the visual.

Parallel analysis: simulate random data of the same size, extract eigenvalues, and compare to the 95th percentile of the random distribution. Retain factors whose eigenvalue exceeds the threshold. This is more accurate than eigenvalue > 1, especially with small samples or few variables.

Cross-check all three methods. If parallel analysis suggests two factors but your data are a three-factor model from the literature, three may be correct even if the third eigenvalue is below 1.

Let KyroStat do the write-up for you

KyroStat runs principal axis factoring on your items, keeps factors with eigenvalue above 1 unless you set the number, applies the rotation you choose, and reports KMO, Bartlett's test, the loadings, the extraction communalities and the eigenvalues of the unreduced matrix. Parallel analysis, item decisions and per-subscale alpha are still yours to check, using the steps above.

Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal

Frequently asked questions

What is KMO and what counts as good? KMO (Kaiser-Meyer-Olkin) measures whether variables share common factors. Kaiser's rule: KMO ≥ .90 marvelous, ≥ .80 meritorious, ≥ .70 middling, ≥ .60 mediocre, ≥ .50 miserable, < .50 unacceptable. KMO below .60 suggests variables are too independent for factor analysis.

What does Bartlett's test do? Bartlett's test checks whether the correlation matrix differs significantly from an identity matrix (no correlations). p > .05 suggests variables are too independent; factor analysis is unhelpful. Published EFA studies almost always have Bartlett's p < .001.

What is the difference between PCA and EFA? Principal components analysis (PCA) reduces dimensionality: it summarizes observed variables into uncorrelated components. Exploratory factor analysis (EFA) assumes latent common factors underlie the observed variables. Use PCA for data reduction; use EFA (with PAF or maximum likelihood) if you believe items measure underlying constructs. Never call PCA "factor analysis."

What are parallel analysis and the Kaiser criterion? The Kaiser criterion retains factors with eigenvalue > 1 (from the unreduced matrix). Parallel analysis simulates random data of the same size and uses the 95th percentile eigenvalues as a threshold. Parallel analysis is more accurate, especially with small N or few items, and is increasingly preferred.

What if an item has a low communality? Communality < .40 means the item is not well-explained by the factors. Consider removing it, re-running the analysis, and reporting both solutions (with and without). Low communality often signals an ambiguous or off-topic item.

Should I use varimax or oblimin? Varimax (orthogonal) produces uncorrelated factors and is simpler to report. Oblimin or Promax (oblique) allow factors to correlate, which is more realistic if constructs overlap. Choose based on theory. Always state which you used.

What sample size do I need? Roughly, N = 20 per item if items are strong (loadings .50 to .80), or N = 50 per item if weak. For 12 items, N = 240 to 600 is typical. Samples below 100 are risky; above 1,000 may detect trivial factors. Always report N clearly.

How do I score individuals on the factors? In SPSS, tick "Save Factor Scores" to create new variables with each person's factor scores. These are regression-weighted linear combinations of the standardized items, not the loadings themselves. Use these scores in subsequent analyses.

What does "a factor's sign is arbitrary" mean? You can multiply all loadings in a column by −1 without changing the analysis. A positive vs. negative sign is a choice you make; do not read meaning into it. Report your chosen sign clearly.

Which related guides might I need? Often: Cronbach's alpha (for subscale reliability), correlation tables (inter-item and inter-factor correlations), descriptive statistics (means and standard deviations), and effect sizes (if comparing factors across groups).