Diagnostics › Agreement

McDonald's omega (reliability)

McDonald's ω estimates model-based reliability from a single-factor model — the modern replacement for Cronbach's α when tau-equivalence is doubtful.

What is McDonald's omega (reliability)?

α assumes every item measures the construct equally well (tau-equivalence); when loadings differ, α underestimates reliability. ω computes reliability from a factor model's loadings and uniquenesses, so unequal loadings are handled correctly.

Computed from a single-factor model; reported alongside α and each item's general-factor loading.

When should I use McDonald's omega (reliability)?

  • Scale reliability for a unidimensional instrument (the recommended default).
  • Whenever you'd report α — ω is the better default.

What data does it need?

≥ 3 numeric item columns.

What does it report?

ω total, ω hierarchical, Cronbach's α (reference), general-factor loading per item.

What does it assume?

  • Unidimensionality (single factor).
  • Continuous (or interval-treated) items.

How do I interpret the result?

ω ≥ 0.8 commonly read as good reliability. A low-loading item suggests it measures something else — consider dropping it.

See also

References

  • McDonald (1999). Test Theory: A Unified Treatment.
  • Dunn, Baguley & Brunsden (2014). From alpha to omega. Br J Psychol 105.