G103 Kolmogorov Test

Subroutine subprogram TKOLMO tests whether two one-dimensional sets of points are compatible with coming from the same parent distribution, using the Kolmogorov test. That is, it is used to compare two experimental distributions of unbinned data.

Structure:

SUBROUTINE subprogram
User Entry Name: TKOLMO
External routine referenced: PROBKL (G102)

Usage:

    CALL TKOLMO(A,NA,B,NB,PROB)

A,B

( REAL) One-dimensional arrays of length NA, NB, respectively. The elements of A and B must be given in ascending order. (This can be accomplished, for example, by using FLPSOR (M103)).

NA,NB

( INTEGER) The number of points in A and B, respectively.

PROB

( REAL) A calculated confidence level which gives a statistical test for compatibility of A and B.

Method:

The Kolmogorov test is used. The test statistic is the maximum deviation between the two integrated distribution functions, multiplied by the normalizing factor $MN/(M+N)$ , where M and N are the numbers of points in the two samples.

Accuracy:

Approximately seven digits are correct.

Notes:

Probabilities smaller than $10-40$ are set to zero. However, the method has a statistical meaning only for "large" M and $N\; (>10)$ .

References:

1. W.T. Eadie, D. Drijard, F.E. James, M. Roos and B. Sadoulet, Statistical Methods in Experimental Physics, (North-Holland, Amsterdam 1971) 269-271.

G104