Cliff’s delta — Worked example

Example data

Group 1: 10 11 9 12 10
Group 2: 8 9 7 10 9

Step-by-step

1. Compare all pairs (x from G1, y from G2).
2. Count wins: gt = #(x>y), losses: lt = #(x<y), ties: eq = #(x=y).
3. Compute delta = (gt − lt) / (n1·n2).
4. Interpret magnitude (rule-of-thumb): |δ| < 0.147 negligible, < 0.33 small, < 0.474 medium, else large.

Intermediate results (illustration)

n1=5, n2=5, total pairs=25.

Most comparisons favor Group 1 in this dataset, so δ will be positive and likely “large”.

Try it in the tool

Open with these values

FAQ

When should I use Cliff’s delta?

When you want an effect size without assuming normality, and you care about dominance/probability-style comparison.

How is it related to Mann–Whitney U?

They’re closely related: both are based on ranks/pairwise comparisons. Cliff’s delta is an interpretable effect size.

Can delta be negative?

Yes—negative means group 2 tends to have larger values than group 1.