Cronbach's Alpha

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.

Loading teaching datasets…

Or use your own dataset

Loading your datasets…

Internal-consistency reliability for a unidimensional set of k items measured on a continuous (interval/ratio) or Likert scale.

Estimates the proportion of total composite-score variance attributable to true-score variance under the essential-tau-equivalence assumption (every item measures the same construct with the same loading magnitude). Reports α with bootstrap 95% CI, item-total correlations, α-if-item-deleted per item, and inter-item correlation matrix. Pair with McDonald's ω when tau-equivalence is doubtful — α is a lower bound on reliability when items differ in factor loading.

Worked example

Is a 10-item anxiety scale internally consistent?

300 respondents completed the 10-item scale; Cronbach's alpha measures how consistently the items tap one construct.

Result

Internal consistency was good, α = .87, 95% CI [.84, .89]; no item's removal would raise alpha, so all 10 items earn their place.

How you'd report it (APA)

The 10-item anxiety scale showed good internal consistency, Cronbach's α = .87.

When to use it

  • Unidimensional Likert composite (single-factor scale)
    A 10-item depression scale administered to 250 patients.
  • Per-subscale reliability after EFA-confirmed factor structure
    A 30-item personality questionnaire decomposes into 5 Big-Five subscales (6 items each) by EFA.

When NOT to — use instead

  • Multi-dimensional scale without subscale decomposition
    α is undefined / misleading on a multi-factor instrument.
  • Binary (0/1) items only
    α reduces to KR-20 on dichotomous items but split-half / KR-20 are the canonical names for that case. → Split-Half (+ KR-20/KR-21)
  • Test-retest reliability (stability over time)
    α is internal consistency, not stability. → Inter-Rater Reliability
  • Inter-rater agreement (multiple raters scoring same subjects)
    α is between-item, not between-rater. → Inter-Rater Reliability

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.

Items share a single underlying factor (unidimensionality)medium

Check: See the assumption diagnostics in the workspace.

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

τ-equivalent loadings (relaxed by McDonald's ω)medium

Check: See the assumption diagnostics in the workspace.

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

Missing data handled by listwise exclusion at the item-set levelmedium

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 Cronbach's Alpha on your own data?

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

Run this test →