In quantitative research โ especially when using survey instruments โ you need to demonstrate that your questionnaire measures what it is intended to measure. This is done by presenting validity evidence through structured tables.
Below are the most common validity tables used in theses, articles, and SPSS/AMOS-based research.
โ Table 1: Convergent Validity Table
This table shows that the items within a construct are highly correlated and share a large amount of variance.
| Construct | CR | AVE | Interpretation |
|---|---|---|---|
| Academic Support | 0.86 | 0.62 | โ Convergent validity established |
| Learning Climate | 0.89 | 0.66 | โ Convergent validity established |
| Motivation | 0.85 | 0.49 | โ ๏ธ AVE < 0.50 โ borderline convergent validity |
| Engagement | 0.92 | 0.71 | โ Strong convergent validity |
๐ Rule of thumb: CR โฅ 0.70 and AVE โฅ 0.50 for acceptable convergent validity
(Hair et al., 2010; Kline, 2015)
โ Table 2: FornellโLarcker Table (Discriminant Validity)
Used to show that constructs are distinct from one another.
| ย | Academic Support | Learning Climate | Motivation |
|---|---|---|---|
| Academic Support | 0.79 | 0.62 | 0.58 |
| Learning Climate | 0.62 | 0.81 | 0.49 |
| Motivation | 0.58 | 0.49 | 0.76 |
๐ Diagonal values are square roots of AVEs. These should be greater than all off-diagonal correlations in their rows/columns.
โ Table 3: HTMT Table (Alternative Discriminant Validity Check)
Optional but increasingly used in newer SEM studies. It compares the HeterotraitโMonotrait ratios between constructs.
| ย | Academic Support | Learning Climate | Motivation |
|---|---|---|---|
| Academic Support | โ | 0.72 | 0.67 |
| Learning Climate | 0.72 | โ | 0.58 |
| Motivation | 0.67 | 0.58 | โ |
๐ HTMT values should be < 0.85 (strict) or < 0.90 (liberal) to confirm discriminant validity
(Henseler, Ringle & Sarstedt, 2015)
โ Table 4: Cross-loading Table (Exploratory Factor Analysis)
When using EFA, cross-loading tables help visualize how strongly each item loads onto each factor.
| 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 |
โ Good items load โฅ 0.50 on their factor and lower on others.
๐ How to Report in Your Thesis
In your Results chapter, place these tables and comment briefly:
โAs 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 FornellโLarcker criterion.โ
๐ Summary of Validity Table Use
| Table Type | Purpose | When to Use |
|---|---|---|
| CR + AVE Table | Convergent validity | Always (after CFA or EFA) |
| FornellโLarcker Table | Discriminant validity | CFA models |
| HTMT Table | Alternative discriminant | CFA (optional/advanced) |
| Cross-loading Table | Factor loading comparisons | EFA models |
