Exploratory factor analysis: interpreting and reporting the output

What question does exploratory factor analysis answer?

Exploratory factor analysis (EFA) examines whether correlations between questionnaire items can be represented by a smaller set of shared factors. It is a measurement question, separate from asking whether two completed scale scores are associated. Principal component analysis (PCA) summarizes observed variation; its components should not be relabelled as latent factors. A high Cronbach alpha does not establish that a scale has one dimension.

The advanced study contains 360 respondents and 15 items about job autonomy, supervisor support and work engagement. Its study brief asks for an exploratory measurement check before scoring the scales and testing H1–H3. The three questionnaire sections are a starting expectation, not instructions to force three factors. This is not a fourth substantive hypothesis.

Read the suitability checks before the factor solution

The example has no missing item values. Calculations use Pearson correlations between its 1–5 items. The choice of correlation matrix matters for ordered responses and should be justified for the actual data, rather than copied from this example.

Overall KMO is 0.896. Bartlett's test gives chi-square(105) = 2207.42, p < .001. KMO compares the correlation pattern with partial correlations; Bartlett tests departure from an identity correlation matrix. These results support examining a factor model here. Neither establishes questionnaire validity or determines the number of factors. The KMO documentation describes both checks. Read item-level results as well as the overall summary, and examine the item meanings and sampling context.

How were three factors considered?

The recorded parallel analysis compares observed factor eigenvalues with simulated reference values. The selected rows below belong to the factor-analysis comparison, not the separate principal-component comparison. See the parallel-analysis documentation.

In the recorded output, the first three exceed their references; the fourth does not. The output therefore suggests three factors. The original correlation-matrix eigenvalues start 5.229, 2.533 and 1.629: they are a different series. Do not mix these columns or use “greater than one” as the sole retention argument. The scree pattern, interpretable solutions and measurement purpose also belong in the decision. Simulated values depend on the analysis settings; the complete record includes seed 1.

Read the rotated pattern without renaming the columns

The fitted example uses minimum residual extraction (MINRES) and oblimin rotation. Oblimin permits correlated factors. The following are three selected items, not the entire loading matrix. Preserve the output's MR1–MR3 labels while connecting the pattern to the item dictionary.

Here q1_1 loads mainly on MR2, q2_1 on MR3 and q3_1 on MR1. Factor numbers are not questionnaire section numbers or an importance ranking. Names require examining all items, their wording and cross-loadings; these three rows alone cannot validate the labels. A loading is not a percentage or a regression effect on the study outcome. Avoid deleting items by a single universal cutoff.

The factor-analysis documentation distinguishes the pattern matrix, structure matrix and factor correlations. In this output, correlations are MR1–MR2 = .404, MR1–MR3 = .489 and MR2–MR3 = .203. Do not interpret the rotated factors as independent or add their contributions as if they were unrelated. Factor signs and order can change in equivalent solutions.

A reporting paragraph with appropriate limits

“An exploratory factor analysis of 15 questionnaire items was conducted for 360 respondents using Pearson correlations, MINRES extraction and oblimin rotation. Overall KMO was .896; Bartlett's test was significant, chi-square(105) = 2207.42, p < .001. Parallel analysis suggested three factors. The complete rotated pattern and factor correlations were reviewed alongside item content before proceeding to the planned scale scores.”

This is a reporting starting point, not external validation. A confirmatory analysis in suitable independent data would address a different question. Scoring decisions and any revisions must be documented, rather than changed silently to improve later results.

Inspect the full record

The measurement request, complete numeric output, findings chapter and decision record let you inspect the full matrices and subsequent steps. See the results-chapter guide for organizing measurement findings separately from hypothesis tests. Outputs depend on the agreed research scope; consultation and ordering remain closed.

See the complete research examples

Follow the research questions through the input files, analysis plan and outputs. Each example includes the consultation report, itemized illustrative price and generated files.