Kolmogorov–Smirnov Test (KS-Test)

Anh-Thi Dinh
This is a quick & dirty draft, for me only!

What & Why?

To check the similar distribution of 2 samples drawn from population. If these samples are normal, we can use T-test, but if they are not normal, we need to use KS-test. KS-test is a non-parametric test.
Null hypothesis (): "Two samples drawn from population with the same distribution."
👉 Read more about p-value. We use this value to evaluate the true/false of above null hypothesis.
The difference (in use) of T-test (need an assumption of nomality) and KS-test (don't need),
  • Two samples have the same mean & standard deviation ⇒ p-value is high ⇒ cannot reject (not true)
  • KS-test can detect the variance ⇒ p-value is low ⇒ we can reject ⇒ 2 samples are not the same distribution!!! (yep!)


If the KS statistic is small or the p-value is high, then we cannot reject the hypothesis that the distributions of the two samples are the same.


1from scipy import stats
1# one-sample KS test
2stats.kstest(x, 'norm')
1# two-sample KS test
2stats.ks_2samp(x, y)


  • An example of why we need to use EMD instead of Kolmogorov–Smirnov distance (video).