A goodness-of-fit test for any Distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally distributed.

To apply the Kolmogorov-Smirnov test, calculate the cumulative frequency (normalized by the sample size) of the observations as
a function of class. Then calculate the cumulative frequency for a true distribution (most commonly, the Normal
Distribution). Find the greatest discrepancy between the observed and expected cumulative frequencies, which is called the
``*D*-Statistic.'' Compare this against the critical *D*-Statistic for that sample size. If the calculated *D*-Statistic is greater than the critical
one, then reject the Null Hypothesis that the distribution is of the expected form. The test is an
*R*-Estimate.

**References**

Boes, D. C.; Graybill, F. A.; and Mood, A. M. *Introduction to the Theory of Statistics, 3rd ed.*
New York: McGraw-Hill, 1974.

Knuth, D. E. §3.3.1B in
*The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 2nd ed.*
Reading, MA: Addison-Wesley, pp. 45-52, 1981.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Kolmogorov-Smirnov Test.'' In
*Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England: Cambridge
University Press, pp. 617-620, 1992.

© 1996-9

1999-05-26