Average Variance Extracted (AVE)
Evaluates convergent validity—how much variance in a set of indicators is explained by the latent construct, relative to measurement error.
Formula
AVE = Σ(λᵢ²) / [ Σ(λᵢ²) + Σ(θᵢ) ]
- λᵢ = standardized factor loading of item i
- λᵢ² = variance explained by the construct
- θᵢ = error (residual) variance of item i
Rule of thumb: AVE ≥ 0.50
Composite Reliability (CR)
Assesses internal consistency reliability using actual loadings (unlike Cronbach’s α).
Formula
CR = [ Σ(λᵢ) ]² / { [ Σ(λᵢ) ]² + Σ(θᵢ) }
- λᵢ = standardized factor loading of item i
- θᵢ = error (residual) variance of item i
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Rule of thumb: CR ≥ 0.70
Quick Calculator
Simulate standardized estimates to see how AVE & CR change.
Separate values with commas (e.g., 0.7, 0.85, 0.6)
*Assumes standardized solution where Error (θ) = 1 - λ²
AVE Result
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CR Result
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Calculation Details:
Enter loadings to see the breakdown.
AVE vs. CR — What’s the difference?
| Feature | AVE | CR |
|---|---|---|
| Validity Focus | Convergent validity (true variance captured) | Reliability (internal consistency) |
| Acceptable Cutoff | ≥ 0.50 | ≥ 0.70 |
| Computation Logic | Uses squared loadings and error variances | Uses sum of loadings and error variances |
Why this matters in your thesis
Documents that constructs are accurately measured (Convergent Validity).
Shows that indicators are consistent (Internal Reliability).
Strengthens the overall credibility of your measurement model.