Composite Reliability

Verified

Reliability (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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Reliability of a latent construct estimated from its factor loadings (CR / ρc) — the SEM-based reliability index.

Composite reliability combines the standardized loadings from a factor / SEM model; unlike alpha it doesn't assume equal loadings. ≥ .70 is acceptable, and it pairs with AVE for convergent validity.

Worked example

Is the 'engagement' construct reliably measured?

From a CFA, the five engagement items' standardized loadings were combined into composite reliability.

Result

CR = .94 (with AVE = .76), indicating strong construct reliability and convergent validity.

How you'd report it (APA)

The engagement construct showed strong composite reliability, CR = .94 (AVE = .76).

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Reliability from a factor / SEM model
    You have a fitted CFA and want reliability that uses the actual standardized loadings rather than assuming they are equal.
  • Congeneric items (unequal loadings)
    When items load on the construct to different degrees, CR (ρc) is more appropriate than Cronbach's alpha.
  • Reporting alongside convergent validity
    CR pairs with AVE (≥ .50) and HTMT for a full convergent/discriminant-validity write-up.

When NOT to — use instead

  • No factor model fitted
    Without loadings, use a raw-score internal-consistency coefficient. → Alpha & Omega
  • Dichotomous test items
    For right/wrong items the KR-20 form is the natural reliability index. → KR-20 / KR-21

Assumptions (and what to do if they fail)

A well-fitting, unidimensional measurement modelhigh

Check: CR is only meaningful if the CFA for that construct fits and the items are unidimensional.

If violated: CR computed on a mis-fitting or multidimensional model overstates reliability.

Standardized loadings are the inputhigh

Check: The formula uses standardized loadings; feeding unstandardized ones gives a wrong ρc.

If violated: The index is on the wrong scale and the ≥ .70 benchmark no longer applies.

CR does not prove validitymedium

Check: High CR means consistent measurement, not that the construct is the right one — read it with AVE and discriminant validity.

If violated: A reliable measure of the wrong thing still looks excellent on CR alone.

Ready to run a Composite Reliability on your own data?

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