Discriminant validity asks a simple question: are your constructs really different from one another? If "job satisfaction" and "organizational commitment" correlate at .92 in your data, respondents may not be able to tell them apart, and any path between them in a structural model is hard to interpret.
Reviewers of survey-based papers almost always ask for evidence of discriminant validity. This guide explains the two main approaches, the Fornell-Larcker criterion and the heterotrait-monotrait ratio (HTMT), the thresholds to use, and what to do when a pair of constructs fails.
In this guide
Where discriminant validity fits
Discriminant validity is the last step of evaluating a measurement model (in CFA, CB-SEM or PLS-SEM). The usual order is:
- Indicator reliability: standardized loadings, ideally ≥ .70.
- Internal consistency reliability: Cronbach's alpha and composite reliability (CR) ≥ .70. See our Cronbach's alpha guide.
- Convergent validity: average variance extracted (AVE) ≥ .50, meaning the construct explains at least half the variance of its items.
- Discriminant validity: each construct is empirically distinct from the others.
Method 1: The Fornell-Larcker criterion
Fornell and Larcker (1981) proposed that a construct should share more variance with its own items than with any other construct. In practice:
The square root of each construct's AVE should be greater than its correlations with every other construct.
You build a table with √AVE on the diagonal and the construct correlations below it.
| SAT | COM | TI | |
|---|---|---|---|
| Satisfaction (SAT) | 0.81 | ||
| Commitment (COM) | 0.62 | 0.78 | |
| Turnover intention (TI) | −0.48 | −0.55 | 0.84 |
Each diagonal value is larger than the correlations in its row and column, so the criterion is met.
A closely related check from Hair et al. compares AVE with the maximum shared variance (MSV), the largest squared correlation with any other construct. Discriminant validity is supported when AVE > MSV.
The problem with Fornell-Larcker
Simulation studies (Henseler, Ringle & Sarstedt, 2015) showed that the Fornell-Larcker criterion often fails to detect discriminant validity problems, especially when loadings are similar across items, which is common with well-designed scales. That is why HTMT is now the recommended primary test, with Fornell-Larcker reported as a supplement.
Method 2: The HTMT ratio
The heterotrait-monotrait ratio compares:
- the average correlation between items of different constructs (heterotrait–heteromethod correlations), with
- the average correlation between items of the same construct (monotrait–heteromethod correlations).
HTMT(i, j) = mean between-construct item correlation ÷ √(mean within-construct correlation of i × mean within-construct correlation of j)
HTMT estimates what the correlation between two constructs would be if they were measured perfectly. Values close to 1 mean the constructs are not distinct.
HTMT thresholds
| Criterion | Rule | When to use |
|---|---|---|
| HTMT.85 | HTMT < 0.85 | Conceptually distinct constructs (conservative) |
| HTMT.90 | HTMT < 0.90 | Conceptually similar constructs (e.g. different facets of satisfaction) |
| HTMT inference | Upper bound of the bootstrap CI < 1 | Formal test; least strict |
Example HTMT matrix:
| SAT | COM | TI | |
|---|---|---|---|
| Satisfaction (SAT) | |||
| Commitment (COM) | 0.71 | ||
| Turnover intention (TI) | 0.54 | 0.63 |
All values are below 0.85, so discriminant validity is established.
How to calculate HTMT and Fornell-Larcker for free
- HTMT calculator: paste your item-level data, define which items belong to which construct, and get the full HTMT matrix together with Fornell-Larcker, AVE, MSV and CR.
- Composite reliability and AVE calculator: if you already have standardized loadings from your SEM software.
- Reliability and validity analysis: alpha, omega, CR, AVE, HTMT and Fornell-Larcker for every construct in one table.
- Inside a full model: CB-SEM Studio and PLS-SEM Studio report all of these as part of the measurement model.
What to do if discriminant validity fails
- Check the theory first. Are the two constructs really different concepts, or two labels for the same thing? Sometimes merging them is the honest answer.
- Look for cross-loading items. An item that loads strongly on both constructs blurs the line between them. Inspect the cross-loadings or modification indices, and consider dropping the item if theory supports it.
- Look at item wording. Items with near-identical wording across scales inflate the correlation.
- Consider common method bias. If everything was measured in a single self-report survey, correlations can be inflated across the board. Run Harman's single-factor test as a first check, and report it.
- Use HTMT.90 if the constructs are conceptually close, and say so explicitly.
- Report it honestly. If a pair exceeds the threshold and you keep both constructs, justify why and discuss it as a limitation.
How to report discriminant validity
Include both tables (Fornell-Larcker and HTMT) and one or two sentences such as:
Discriminant validity was assessed with the Fornell-Larcker criterion and the heterotrait-monotrait ratio (HTMT). The square root of each construct's AVE exceeded its correlations with all other constructs, and all HTMT values were below the conservative threshold of 0.85 (highest HTMT = 0.71, between satisfaction and commitment). Discriminant validity was therefore established (Fornell & Larcker, 1981; Henseler et al., 2015).
References to cite
- Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50.
- Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43(1), 115–135.
Frequently asked questions
What is the HTMT threshold for discriminant validity?
Use 0.85 for conceptually distinct constructs and 0.90 for conceptually similar ones. A more lenient test checks that the upper bound of the bootstrapped HTMT confidence interval is below 1.
Is the Fornell-Larcker criterion still accepted?
It is still reported, but research has shown it often misses discriminant validity problems. Report HTMT as your main criterion and Fornell-Larcker as supporting evidence.
What is the difference between convergent and discriminant validity?
Convergent validity shows that items of the same construct agree with each other (AVE ≥ .50). Discriminant validity shows that different constructs are distinct from each other (for example HTMT < .85).
Can I use HTMT in CB-SEM as well as PLS-SEM?
Yes. HTMT is computed from item correlations, so it works with any measurement model: CFA, CB-SEM or PLS-SEM.