KMO + Bartlett

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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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Pre-EFA / pre-CFA screening: are the items factor-analysable at all?

Two complementary statistics: (1) Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy quantifies the proportion of variance among variables that may be common variance — KMO ≥ 0.60 is acceptable, ≥ 0.80 is meritorious. (2) Bartlett's test of sphericity tests whether the correlation matrix is significantly different from an identity matrix — Bartlett p < .05 means there IS shared variance to extract. Both must pass before factor analysis is interpretable. Reports overall KMO, per-item MSA (low MSAs flag items to drop), and Bartlett χ² + df + p.

Worked example

Is the data suitable for factor analysis?

Before factoring, the KMO statistic measures sampling adequacy and Bartlett's test checks that the correlation matrix isn't an identity.

Result

The data were factorable: KMO = .89 (meritorious), Bartlett's χ²(153) = 2840, p < .001.

How you'd report it (APA)

Sampling adequacy was excellent (KMO = .89) and Bartlett's test was significant, χ²(153) = 2840, p < .001, supporting factor analysis.

When to use it

  • Pre-EFA factorability screen (default use)
    Candidate 25-item personality scale on n=400.
  • Item-pruning by per-item MSA
    30-item scale screen: overall KMO = 0.78.

When NOT to — use instead

  • Already running EFA / CFA — KMO not requested
    If you've already decided to run factor analysis (or are reporting a fitted model), KMO is descriptive context. → Exploratory FA
  • Reliability assessment (not factorability)
    KMO is about whether items share variance. → Cronbach's Alpha
  • Single-item or very few-item set (k < 4)
    KMO + Bartlett need enough items to form a meaningful correlation matrix — k ≥ 4 is the practical floor. → CTT Item Analysis
  • Tiny sample (n < 100)
    Both statistics are unstable on small n. → Parallel Analysis

Assumptions (and what to do if they fail)

Items measured on a continuous / interval-like scalemedium

Check: See the assumption diagnostics in the workspace.

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

Sample size ≥ 100 (Kaiser 1974) and ideally n:p ≥ 10 (Nunnally 1994)medium

Check: See the assumption diagnostics in the workspace.

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

No zero-variance or perfectly collinear itemsmedium

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 KMO + Bartlett on your own data?

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

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