Kolmogorov test

From HandWiki


A powerful test (also called Kolmogorov-Smirnov test) that a one-dimensional data sample is compatible with being a random sampling from a given distribution. It is also used to test whether two data samples are compatible with being random samplings of the same, unknown distribution. It is similar to the Cramer-Smirnov-Von-Mises test, but somewhat simpler.

To compare a data sample consisting of N events whose cumulative distribution is SN(x) with a hypothesis function whose cumulative distribution is F(x), the value DN is calculated:

Hepa img540.gif

The confidence levels for some values of Hepa img541.gif are (for N > 80):

conf.l. Hepa img541.gif
10% 1.22
5% 1.36
1% 1.63

To compare two experimental cumulative distributions SN(x) containing N events, and SM(x) containing M events, calculate:

Hepa img542.gif

Then Hepa img543.gif is the test statistic for which the confidence levels are as in the above table. For more detail, Hepa img1.gif Press95.