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Cliff’s delta (effect size)
Non-parametric effect size: (P(X>Y) − P(X<Y)). Based on all pairwise comparisons.
Inputs
Group 1 values
10 11 9 12 10
Group 2 values
8 9 7 10 9
Compute
Delta ranges from −1 to +1. Positive means Group 1 tends to be larger.
Result
Computed ✅
n1:
5 ·
n2:
5
#(x>y):
20 ·
#(x<y):
1 ·
#(x=y):
4
Cliff’s delta:
0.76
Magnitude:
large
Interpretation:
large effect (rule-of-thumb). Positive means group 1 tends to be larger.
Step-by-step
Count pairwise dominance
Formula:
Compare all pairs (x in G1, y in G2)
Substitute:
Total pairs = 5·5 = 25
Result:
gt=20, lt=1, eq=4
Compute Cliff’s delta
Formula:
δ = (gt − lt) / (n1·n2)
Substitute:
(20 − 1) / 25
Result:
δ = 0.76
Magnitude (rule-of-thumb)
Formula:
|δ| thresholds: 0.147, 0.33, 0.474
Substitute:
|δ| = 0.76
Result:
large
