Calculator Form
Use commas, spaces, semicolons, or line breaks between numbers.
Example Data Table
Use this sample dataset to test the calculator quickly.
| Observation | Group A | Group B |
|---|---|---|
| 1 | 12 | 10 |
| 2 | 15 | 11 |
| 3 | 16 | 12 |
| 4 | 14 | 13 |
| 5 | 18 | 14 |
| 6 | 19 | 15 |
| 7 | 20 | 16 |
| 8 | 17 | 12 |
Formula Used
Cliff's Delta measures dominance between two independent groups. It compares every value in Group A with every value in Group B.
δ = (number of pairs where xi > yj − number of pairs where xi < yj) / (nA × nB)
- δ = 1 means Group A dominates Group B completely.
- δ = -1 means Group B dominates Group A completely.
- δ ≈ 0 means little or no dominance difference.
This calculator also reports a bootstrap confidence interval, tie rate, common language probabilities, and a practical interpretation using adjustable thresholds.
How to Use This Calculator
- Enter a label for each group.
- Paste numeric values into both sample boxes.
- Choose decimal precision, confidence level, and bootstrap iterations.
- Adjust interpretation thresholds if needed.
- Click the calculate button.
- Review the effect size, interval, comparison counts, and chart.
- Export the report using the CSV or PDF buttons.
FAQs
1) What does Cliff's Delta measure?
It measures how strongly one group tends to have larger values than another group. It is an effect size for ordinal or continuous data and does not require normal distributions.
2) When should I use Cliff's Delta?
Use it when comparing two independent groups and you want a nonparametric effect size. It is useful when data are skewed, contain outliers, or are measured on an ordinal scale.
3) Can the two groups have different sample sizes?
Yes. Cliff's Delta works with unequal group sizes because it evaluates all possible pairwise comparisons between the two samples.
4) What does a positive delta mean?
A positive result means Group A tends to contain larger values than Group B. A negative result means Group B tends to contain larger values instead.
5) Why is a confidence interval included?
The interval shows uncertainty around the estimated effect size. Narrow intervals suggest a more stable estimate, while wider intervals suggest more sampling variability.
6) How are ties handled in the calculation?
Tied comparisons are counted separately. They reduce dominance strength because tied pairs do not support either group as being larger.
7) Is Cliff's Delta the same as a significance test?
No. It measures effect size, not statistical significance. You can use it alongside tests such as Mann-Whitney when you also need inferential evidence.
8) What interpretation thresholds are used here?
The default thresholds are 0.147, 0.330, and 0.474 for negligible, small, and medium effects. Values above 0.474 are treated as large. You can edit these cutoffs directly.