Kolmogorov-Smirnov(K-S) Test

Comparing Distributions

4 min readMar 30, 2021

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Kolmogorov-Smirnov(K-S) test

In statistics, Kolmogorov-Smirnov(K-S) test is a non-parametric test of the equality of the continuous, one-dimensional (univariate) probability distributions.

K-S test compares the two cumulative distributions and returns the maximum difference between them.

One-sample K-S test or goodness of fit test was developed by Andrey Nikolayevich Kolmogorov in 1933. Its purpose is to compare the overall shapes of two sample distributions.

Two-sample K-S test was developed by Nikolai Smirnov in 1939. Its purpose is to compare one sample to a known statistical distribution.

Parametric and non-parametric statistics

We can separate the statistical tests into two: Parametric and non-parametric tests.

Parametric tests are suitable for normally distributed data and they have more statistical power than nonparametric ones.

• Independent samples t-test and paired samples t-test
• ANOVA
• Regression

Nonparametric tests or distribution-free tests are suitable for any continuous data. They can be used with a very small sample size…

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