McDonald's Omega

Verified

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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Modern reliability coefficient that relaxes Cronbach's α's essential-tau-equivalence assumption — items are allowed to have DIFFERENT factor loadings on the underlying construct.

Computes ω from a single-factor CFA of the items: ω = (Σλ_i)² / [(Σλ_i)² + Σθ_ii], where λ_i are standardised loadings and θ_ii are residual variances. Reports ω with bootstrap 95% CI, hierarchical ω_h (proportion of variance from a general factor in a bifactor model), and ω_total (general + group factors). The current best-practice reliability estimate for psychological measurement.

Worked example

What is the reliability without assuming all items load equally?

McDonald's omega estimates reliability from a factor model, avoiding Cronbach's alpha's tau-equivalence assumption.

Result

Reliability was good, ω = .89 — slightly above alpha (.87), as expected when loadings differ.

How you'd report it (APA)

McDonald's omega indicated good reliability, ω = .89.

When to use it

  • Unidimensional scale with loading heterogeneity
    12-item self-esteem scale where loading magnitudes range from 0.45 to 0.85 (substantial heterogeneity).
  • Bifactor model — ω_h general-factor strength
    20-item depression scale with 4 group factors (somatic, cognitive, affective, interpersonal).

When NOT to — use instead

Assumptions (and what to do if they fail)

Items measured on a continuous / Likert scale (or treat as approximately interval)medium

Check: See the assumption diagnostics in the workspace.

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

A hypothesised factor structure (unidimensional or bifactor)medium

Check: See the assumption diagnostics in the workspace.

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

Model fit is acceptable (CFI ≥ .90, SRMR ≤ .08 as minimum)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.

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