Validity Evidence in
Quantitative Research
In quantitative research—especially when using survey instruments—you must demonstrate that your questionnaire measures what it is intended to measure. We do this by presenting structured validity evidence.
Convergent Validity
Shows that items within a construct are highly correlated.
| Construct | CR (Composite Reliability) | AVE (Avg Variance Extracted) | Interpretation |
|---|---|---|---|
| Academic Support | 0.86 | 0.62 | Established |
| Learning Climate | 0.89 | 0.66 | Established |
| Motivation | 0.85 | 0.49 | Borderline (AVE < 0.50) |
| Engagement | 0.92 | 0.71 | Strong |
Rule of Thumb
CR ≥ 0.70 and AVE ≥ 0.50 for acceptable convergent validity.
(Hair et al., 2010; Kline, 2015)
Fornell–Larcker Criterion
Proves constructs are distinct from one another.
| Acad. Support | Learn. Climate | Motivation | |
|---|---|---|---|
| Acad. Support | 0.79 | 0.62 | 0.58 |
| Learn. Climate | 0.62 | 0.81 | 0.49 |
| Motivation | 0.58 | 0.49 | 0.76 |
Diagonal values (bold) are square roots of AVEs. These should be greater than all off-diagonal correlations in their rows/columns.
HTMT Criterion
Heterotrait–Monotrait ratio (Newer standard).
| AS | LC | MOT | |
|---|---|---|---|
| AS | - | 0.72 | 0.67 |
| LC | 0.72 | - | 0.58 |
| MOT | 0.67 | 0.58 | - |
Thresholds
- < 0.85 (Strict criterion)
- < 0.90 (Liberal criterion)
(Henseler, Ringle & Sarstedt, 2015)
Cross-loading Table (EFA)
| Item | Factor 1: Support | Factor 2: Motivation | Factor 3: Engagement |
|---|---|---|---|
| S1 | 0.78 | 0.42 | 0.35 |
| S2 | 0.81 | 0.38 | 0.22 |
| M1 | 0.29 | 0.76 | 0.30 |
| E1 | 0.32 | 0.25 | 0.84 |
✅ Good items load ≥ 0.50 on their primary factor and lower on others.
📌 How to Report in Your Thesis
In your Results chapter, place the tables and comment briefly:
“As shown in Table 1, all constructs met the threshold for convergent validity with CR > 0.70 and AVE > 0.50, except for Motivation which showed marginally acceptable AVE. Table 2 confirms discriminant validity as all diagonal values exceed corresponding correlations, in line with the Fornell–Larcker criterion.”
Use Case Summary
- CR + AVE Convergent Validity (Always)
- Fornell–Larcker Discriminant Validity (CFA)
- HTMT Modern Discriminant (Optional)
- Cross-loading Factor Loading (EFA)