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Vargha–Delaney A12

Probability that a randomly chosen value from Group 1 exceeds a randomly chosen value from Group 2 (ties count as 0.5).

Inputs

A12=0.5 means no dominance; >0.5 favors Group 1; <0.5 favors Group 2.

Result

Computed ✅
n1: 4 · n2: 4
#(x>y): 15 · #(x<y): 0 · #(x=y): 1
A12: 0.9688
Interpretation: A12 > 0.5 favors group 1; A12 < 0.5 favors group 2. 0.5 means no dominance.
Step-by-step

  1. Count pairwise wins and ties

    Formula: Compare all pairs (x in G1, y in G2)
    Substitute: Total pairs = 4·4 = 16
    Result: gt=15, lt=0, eq=1

  2. Compute Vargha–Delaney A12

    Formula: A12 = (gt + 0.5·eq) / (n1·n2)
    Substitute: (15 + 0.5·1) / 16
    Result: A12 = 0.9688
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