SEM / CFA Validity Check

The Fornell–Larcker Criterion

The gold standard for assessing discriminant validity in structural equation modeling. Ensure your constructs are distinct and statistically robust.

The Core Logic

It checks whether each construct is sufficiently distinct from other constructs in the model. The logic is simple: a construct should share more variance with its own indicators than with any other construct.

// The Formula

\(\sqrt{AVE_i} > |r_{ij}|\)

for all \(i \neq j\)

Note: Use latent construct correlations (ϕ) from your AMOS output, not raw item correlations.

Construct A √AVE High
Construct B
Low Correlation

📊 Interactive Fornell–Larcker Matrix

Hover over the bold diagonal values (√AVE) to see which correlations they must exceed.

Construct Construct A Construct B Construct C
A 0.76 (√AVE) 0.43 0.51
B 0.43 0.72 (√AVE) 0.39
C 0.51 0.39 0.80 (√AVE)
Result: Discriminant validity supported (all √AVEs > correlations).

Validity Checker

Enter your constructs' values below to see if they pass the Fornell-Larcker criterion.

Waiting for input...

Square Root of AVE: -

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🧰 Workflow: From AMOS to Excel

1

AMOS Setup

Go to Analysis Properties → Output. Tick Standardized estimates before running the model.

2

Copy Data

Paste latent variances and covariances into the template's yellow cells.

3

Auto-Calc

The template computes AVE and CR. Optionally paste standardized loadings (λ) for precision.

4

The Matrix

Review the generated table. Check for the "PASS" indicator and copy to your manuscript.

Download Excel Template

Construct order: Usability → Effectiveness → Engagement

Common Pitfalls

  • Low AVE (< 0.50): Weakens both convergent and discriminant validity.
  • High Correlations: If |rij| ≥ √AVE, constructs overlap conceptually.
  • Wrong Metrics: Avoid mixing item correlations with latent √AVE.

Quick Recap

Metric Purpose Rule
AVE Convergent ≥ 0.50
F-L Criterion Discriminant √AVE > |r|