Enter paired scores
Use equal-length predictor and criterion score lists. Separate numbers with commas, spaces, or line breaks.
Example data table
This example shows paired test and criterion scores that can be pasted directly into the calculator.
| Case | Predictor score | Criterion score |
|---|---|---|
| 1 | 45 | 48 |
| 2 | 50 | 51 |
| 3 | 52 | 55 |
| 4 | 57 | 58 |
| 5 | 60 | 61 |
| 6 | 63 | 65 |
| 7 | 67 | 66 |
| 8 | 70 | 72 |
| 9 | 74 | 75 |
| 10 | 78 | 80 |
Formula used
Pearson criterion validity coefficient
r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √[Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²]
Significance test for r
t = r × √[(n − 2) / (1 − r²)], with df = n − 2
Shared variance
R² = r²
Simple regression line
ŷ = a + bx, where b = Cov(x,y) / Var(x) and a = ȳ − bx̄
Standard error of estimate
SEE = √[Σ(y − ŷ)² / (n − 2)]
Disattenuated validity coefficient
rcorrected = r / √(reliabilityx × reliabilityy)
Criterion validity measures how strongly a test or predictor score relates to an external criterion. Larger absolute coefficients indicate better validity evidence, while R² shows how much criterion variation is explained.
How to use this calculator
- Choose whether you are evaluating predictive or concurrent validity.
- Enter matching predictor and criterion score lists in the two text areas.
- Select the confidence level and hypothesis direction for your test.
- Set a benchmark validity coefficient if you need a pass or fail decision.
- Optionally provide reliability estimates to compute a corrected validity coefficient.
- Click the calculate button to display results above the form.
- Review the coefficient, interval, significance, regression, and plotted relationship.
- Export the summary or full paired dataset as CSV, or save the result area as a PDF.
FAQs
1. What does criterion validity mean?
Criterion validity shows how well a test score relates to an external outcome or standard. It is commonly used to check whether a measure predicts or matches real performance.
2. What is the difference between predictive and concurrent validity?
Predictive validity links current scores to future outcomes. Concurrent validity compares scores with a criterion measured at the same time. Both are forms of criterion-related evidence.
3. When should I use Pearson r here?
Use Pearson r when both variables are numeric and the relationship is approximately linear. It is the standard coefficient for many criterion validity studies.
4. Why does the calculator also report Spearman rho?
Spearman rho checks rank-order agreement. It is useful when scores are skewed, tied, or not perfectly linear. Comparing both coefficients can reveal whether the validity pattern is stable.
5. What is a good criterion validity coefficient?
There is no universal cut point. In many applied settings, coefficients near 0.30 may be useful, while higher stakes decisions often demand stronger evidence and narrower confidence intervals.
6. Why is the confidence interval important?
The interval shows uncertainty around the observed coefficient. A narrow interval suggests more stable evidence, while a wide interval signals that the sample may be too small or noisy.
7. What does the corrected validity coefficient do?
It adjusts the observed relationship for measurement error using the reliability of both variables. This estimate can show the underlying association when scores are imperfectly measured.
8. Can I export the results for reporting?
Yes. The page includes summary CSV export, dataset CSV export, and a PDF option. These help you document coefficients, intervals, plots, predictions, and residuals.