{"id":1023,"date":"2026-10-14T01:16:00","date_gmt":"2026-10-14T01:16:00","guid":{"rendered":"https:\/\/freestatisticaltools.com\/blog\/?p=1023"},"modified":"2026-10-14T01:16:00","modified_gmt":"2026-10-14T01:16:00","slug":"discriminant-validity-htmt-fornell-larcker","status":"publish","type":"post","link":"https:\/\/freestatisticaltools.com\/blog\/discriminant-validity-htmt-fornell-larcker\/","title":{"rendered":"Discriminant Validity: HTMT vs Fornell-Larcker (and What Thresholds to Use)"},"content":{"rendered":"\n

Discriminant validity<\/strong> 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.<\/p>\n\n\n\n

Reviewers of survey-based papers almost always ask for evidence of discriminant validity. This guide explains the two main approaches, the Fornell-Larcker criterion<\/strong> and the heterotrait-monotrait ratio (HTMT)<\/strong>, the thresholds to use, and what to do when a pair of constructs fails.<\/p>\n\n\n

<\/svg><\/span>Free tool \u00b7 runs in your browser<\/span>HTMT Calculator for Discriminant Validity<\/a>Free HTMT calculator: heterotrait\u2013monotrait ratio for every pair of constructs, with Fornell\u2013Larcker, AVE, MSV and composite reliability from your item data.<\/span><\/span>Calculate HTMT \u2192<\/a><\/div>\n\n\n\n

Where discriminant validity fits<\/h2>\n\n\n\n

Discriminant validity is the last step of evaluating a measurement model<\/strong> (in CFA, CB-SEM or PLS-SEM). The usual order is:<\/p>\n\n\n\n

    \n
  1. Indicator reliability:<\/strong> standardized loadings, ideally \u2265 .70.<\/li>\n\n
  2. Internal consistency reliability:<\/strong> Cronbach's alpha and composite reliability (CR) \u2265 .70. See our Cronbach's alpha guide<\/a>.<\/li>\n\n
  3. Convergent validity:<\/strong> average variance extracted (AVE) \u2265 .50, meaning the construct explains at least half the variance of its items.<\/li>\n\n
  4. Discriminant validity:<\/strong> each construct is empirically distinct from the others.<\/li>\n<\/ol>\n\n\n\n

    Method 1: The Fornell-Larcker criterion<\/h2>\n\n\n\n

    Fornell and Larcker (1981) proposed that a construct should share more variance with its own items than with any other construct. In practice:<\/p>\n\n\n\n

    The square root of each construct's AVE should be greater than its correlations with every other construct.<\/p><\/blockquote>\n\n\n\n

    You build a table with \u221aAVE on the diagonal and the construct correlations below it.<\/p>\n\n\n\n

    <\/th>SAT<\/th>COM<\/th>TI<\/th><\/tr><\/thead>
    Satisfaction (SAT)<\/td>0.81<\/strong><\/td><\/td><\/td><\/tr>
    Commitment (COM)<\/td>0.62<\/td>0.78<\/strong><\/td><\/td><\/tr>
    Turnover intention (TI)<\/td>\u22120.48<\/td>\u22120.55<\/td>0.84<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Each diagonal value is larger than the correlations in its row and column, so the criterion is met.<\/p>\n\n\n\n

    A closely related check from Hair et al. compares AVE with the maximum shared variance (MSV)<\/strong>, the largest squared correlation with any other construct. Discriminant validity is supported when AVE > MSV.<\/p>\n\n\n\n

    The problem with Fornell-Larcker<\/h3>\n\n\n\n

    Simulation studies (Henseler, Ringle & Sarstedt, 2015) showed that the Fornell-Larcker criterion often fails to detect<\/strong> 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.<\/p>\n\n\n\n

    Method 2: The HTMT ratio<\/h2>\n\n\n\n

    The heterotrait-monotrait ratio<\/strong> compares:<\/p>\n\n\n\n