Factor-model-based reliability that allows items to load unequally — the recommended modern replacement for (or companion to) Cronbach's alpha.
Measure ReliabilityMultivariatealso known as: Omega total, ω, Omega hierarchical
✓ When to use
Whenever you would report alpha — omega relaxes alpha's unrealistic equal-loading assumption.
Items with visibly unequal loadings in CFA.
Hierarchical scales (general factor + group factors): omega-hierarchical quantifies how much variance the general factor alone explains.
✗ When NOT to use
No factor model can be estimated (tiny samples, ill-conditioned data).
Formative indices.
Two-item scales — Spearman–Brown.
When the factor model badly misfits — fix the model before computing reliability from it.
Data requirements
Dependent / outcome variable
k ≥ 3 reflective items of one construct (or a bifactor structure for ω-hierarchical).
Independent / grouping variable
—
Design
One administration.
Sample size guidance
Enough for stable CFA estimation (typically n ≥ 150–200).
Assumptions
A congeneric measurement model fits: one factor, freely estimated loadings.
Uncorrelated errors unless explicitly modeled.
Continuous-ish items (use categorical omega variants for few-point ordinal items).
Hypotheses
H₀ — — (estimate with CI, not a test).
H₁ — —
The concept
Omega total = (Σλ)² / [(Σλ)² + Σθ], where λ are standardized factor loadings and θ are residual variances: the share of total score variance attributable to the common factor when each item is allowed its own loading. When loadings truly are equal, omega equals alpha; when they differ, alpha understates reliability and omega corrects it.
For scales with a general factor plus content clusters, omega-hierarchical isolates the general factor's share — crucial before interpreting a total score as measuring 'one thing'. Methodologists (e.g., McNeish 2018; Flora 2020) now recommend omega as the default reliability statistic; journals increasingly ask for it alongside or instead of alpha.
Worked example
The 6-item commitment scale's CFA shows loadings from .58 to .84 — clearly unequal, so alpha (.86) is a lower bound.
Result: ω = .88, 95% CI [.85, .90], confirming strong internal consistency under realistic assumptions.
How to run it
library(psych)
omega(df[, paste0("ac", 1:6)], nfactors = 1) # omega total (+ alpha)
# from a lavaan CFA:
library(semTools)
fit <- cfa('commit =~ ac1+ac2+ac3+ac4+ac5+ac6', data = df)
reliability(fit) # omega, alpha, AVE
# omega hierarchical for bifactor scales: psych::omega(items, nfactors = 3)
# via reliabiliPy (pip install reliabilipy)
from reliabilipy import reliability_analysis
ra = reliability_analysis(correlations_matrix=df[items].corr())
ra.fit()
print(ra.omega_total, ra.alpha_cronbach)
Older SPSS: install Hayes's OMEGA macro (from processmacro.org resources) or compute from Amos CFA loadings: ω = (Σλ)²/((Σλ)² + Σ(1−λ²)) using standardized estimates.
Report ω with CI where available, alongside α.
From CFA standardized loadings: ω = (SUM(λ))^2 / ((SUM(λ))^2 + SUM(1−λ^2)).
Enter the loadings in a column and apply the formula; no CI available this way.
Interpreting the output
Same benchmarks as alpha (≥ .70 / .80).
ω ≥ α is typical; a large gap flags unequal loadings.
ω-hierarchical ≥ .70–.75 supports interpreting a total score despite multidimensionality.
Report the measurement model it came from.
APA-style reporting
Internal consistency was high, McDonald's ω = .88, 95% CI [.85, .90] (Cronbach's α = .86), computed from a single-factor model with standardized loadings between .58 and .84.
Common mistakes
Computing omega from a misfitting one-factor model.
Confusing omega total with omega hierarchical in multidimensional scales.
Treating omega as exotic — it is standard and expected in current practice.
Reporting omega without stating the underlying model.