Kolmogorov test

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 S_N(x) with a hypothesis function whose cumulative distribution is F(x), the value D_N is calculated:

The confidence levels for some values of are (for N > 80):

conf.l.
10%	1.22
5%	1.36
1%	1.63

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

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