Exploratory FA

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Psychometrics (legacy hub)

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Latent-factor extraction from a set of correlated items WITHOUT a priori specification of which items load on which factor.

Reports per-item loading matrix, communalities, factor inter-correlations (with oblique rotation), variance explained per factor, factor-correlation matrix, and the rotated solution. The standard scale-discovery / scale-validation tool. Engine pre-runs parallel analysis to pick factor count, KMO + Bartlett to confirm factorability, and applies oblique (promax) rotation by default — orthogonal (varimax) only when factors are theoretically uncorrelated.

Worked example

How many factors underlie a new 18-item scale?

Exploratory factor analysis (principal-axis extraction, oblimin rotation) on 18 items (n = 350).

Result

Three factors explained 58% of variance; items loaded cleanly (> .45) with minimal cross-loadings.

How you'd report it (APA)

An EFA (principal-axis, oblimin) extracted three interpretable factors explaining 58% of the variance.

When to use it

  • Scale discovery — factor structure unknown
    30-item adapted personality questionnaire on a validation sample (n=400).
  • Scale revision after CFA fails
    5-factor questionnaire CFA fits poorly (CFI = 0.84, RMSEA = 0.10).

When NOT to — use instead

  • Confirmatory test of a hypothesised factor structure
    EFA is exploratory; for a hypothesised model use CFA which tests fit explicitly. → Confirmatory FA
  • Single-factor scale with known structure
    EFA forced to 1 factor is just principal-factor extraction. → McDonald's Omega
  • Sample too small (n < 5 × k)
    EFA needs adequate sample for stable loading estimates. → KMO + Bartlett
  • Items not factor-analysable (KMO < 0.50)
    If KMO + Bartlett fail, the items don't share enough variance for EFA to be meaningful. → KMO + Bartlett

Assumptions (and what to do if they fail)

Items measured on a continuous / Likert scalemedium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Linear relationships between items + factorsmedium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Adequate sample size (n ≥ 200, n:p ≥ 10)medium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Absence of multicollinearity (KMO ≥ .60)medium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Listwise exclusion of incomplete response setsmedium

Check: See the assumption diagnostics in the workspace.

If violated: The workspace flags this and suggests a robust or nonparametric alternative.

Ready to run a Exploratory FA on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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