Kolmogorov-Smirnov Algorithm

Computes the difference of the distributions of two empirical observation sets.

K-S Statistic

  1. $N_1$ is the size of group 1
  2. $N_2$ is the size of group 2

  1. $S_{N_1}(x)$ is the empirical distribution of group 1
  2. $S_{N_2}(x)$ is the empirical distribution of group 2

$D=max_{-\infty<x<\infty}|S_{N_1}(x)-S_{N_2}(x)|\htmlimage{extrascale=1.5}$

K-S Significance

$Q_{KS}(\lambda)=2\Sigma_{j=1}^\infty(-)^{j-1}e^{-2j^2\lambda^2}\htmlimage{extrascale=1.5}$

Probability (D > observed) = $Q_{KS}(\sqrt{\frac{N_1*N_2}{N_1+N_2}}*D)\htmlimage{extrascale=1.5}$
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Topic revision: r3 - 09 Dec 2004, WillGray
 

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