stats

Two-Sample Kolmogorov-Smirnov

Distribution-free two-sample test — D statistic, p-value at α=0.05/0.01, ECDF overlay with D arrow.

Input — Two Samples

Tail

Sample 1 (comma or space separated)Sample 2 (comma or space separated)

Results

n₁ / n₂—

Effective n n₁n₂/(n₁+n₂)—

D statistic (two-tailed)—

p-value—

Conclusion α = 0.05—

Conclusion α = 0.01—

Sample Comparison

Mean (S1 / S2)—

Median (S1 / S2)—

SD (S1 / S2)—

D = max|F̂₁(x) − F̂₂(x)| · n_eff = n₁n₂/(n₁+n₂)
p ≈ 2Σ(−1)^(k+1) exp(−2k²D²n_eff) (two-tailed)
One-sided: p ≈ exp(−2D²n_eff)