User Guide: AVE/CR Calculator

This calculator evaluates convergent validity using composite reliability (CR) and average variance extracted (AVE). When construct correlations are supplied, it also evaluates discriminant validity using the Fornell-Larcker criterion.

1. Calculation Rules

• Composite reliability: CR ≥ .70 meets the recommended minimum.
• Average variance extracted: AVE ≥ .50 meets the recommended minimum.
• Fornell-Larcker: √AVE for each construct must be strictly greater than every absolute correlation involving that construct.

2. Accepted Loading Formats

You may paste the table directly from AMOS, including its headings and numeric latent-variable labels:

Standardized Regression Weights: (Group number 1 - Default model)
   Estimate
EG3 <--- 1 .820
EG2 <--- 1 .786
US3 <--- 2 .789
EF4 <--- 3 .800

When AMOS uses numeric labels such as 1, 2, and 3, the report displays them as Construct 1, Construct 2, and Construct 3. When all indicators share a clear prefix, the prefix is also shown, for example Construct 1 (EG). Rename the latent variables in AMOS to obtain descriptive construct names.

Descriptive AMOS arrow rows are also supported:

U1 <--- Usability .820
U2 <--- Usability .790

A labeled table is also supported:

Item,Construct,Loading
U1,Usability,.820
U2,Usability,.790

Standardized loadings must be between −1 and 1. At least two indicators must be supplied for every construct.

3. Accepted Correlation Formats

Direct AMOS pair rows with numeric labels are accepted:

Correlations: (Group number 1 - Default model)
   Estimate
1 <--> 2 .632
1 <--> 3 .839
2 <--> 3 .695

Rows with descriptive construct names are also accepted:

Usability <--> Effectiveness .695
Usability <--> Engagement .632
Effectiveness <--> Engagement .738

You may also paste a full or triangular labeled correlation matrix. For a complete Fornell-Larcker decision, every pair of constructs must be present.

4. Using the Sample

1. Select Load Sample Data.
2. The sample is inserted into both text areas and calculated immediately.
3. Review the extracted loading table, formula audit, threshold decisions, and pairwise Fornell-Larcker comparisons.

The supplied direct-AMOS sample produces the following rounded results:

5. Reading the Results

The first section reproduces every parsed loading and shows λ² and measurement error. The formula cards display all totals used in CR and AVE. This makes it possible to verify each result manually.

If a loading row cannot be parsed, a construct is missing indicators, a value falls outside the valid standardized range, or correlations conflict, the calculator stops and reports the exact problem instead of making an assumption.

6. When a Criterion Fails

Check the original model output before modifying the measurement model. Common causes include an incorrectly copied value, a reverse-coded item that was not recoded, a low loading, a cross-loading item, or constructs that are not sufficiently distinct. Any item removal or construct revision should be theoretically justified and the model should then be re-estimated.