stats
Kolmogorov-Smirnov Test
One-sample KS test against Normal, Uniform, Exponential, or Poisson — D statistic, p-value, ECDF vs theoretical CDF overlay.
Input
Theoretical distribution
Parameters
Parameters estimated from data — p-value is conservative (test is biased when parameters are not pre-specified)
Results
n—
Distribution—
Parameters—
D statistic—
p-value (two-tailed)—
Conclusion α = 0.05—
Conclusion α = 0.01—
D = max|F̂ₙ(x) − F(x)| · evaluated at each sorted xᵢ
p ≈ 2Σ(−1)^(k+1) exp(−2k²D²n) (Kolmogorov distribution)
Caution: estimating parameters from data inflates Type I error
p ≈ 2Σ(−1)^(k+1) exp(−2k²D²n) (Kolmogorov distribution)
Caution: estimating parameters from data inflates Type I error