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].

Rudolf K. Bock, 7 April 1998