# F Distribution Test (Kolmogorov-Smirnov)

The Kolmogorov-Smirnov test can be used to test the null hypothesis that the population distribution from which the data sample is drawn is an F distribution.

To properly analyze and interpret results of F distribution test by the Kolmogorov-Smirnov test, you should be familiar with the following terms and concepts:

F Distribution:
A distribution that is of fundamental importance in analysis of variance. It arises as the sampling distribution of the ratio of the values of two independent random variables having chi-square distributions, each divided by its degrees of freedom; for example, the ratio of the variances of two random samples from normal populations having the same variance. Correspondingly, the parameters v1 and v2 of the F distribution are referred to as its numerator and denominator degrees of freedom. The F distribution is also known as the variance-ratio distribution.
An F table contains values of Fα,v1,v2 for which (under an appropriate null hypothesis) has an F distribution. See F test, which is a test concerning the equality of two population variances.

If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Failure to understand and properly apply F distribution test by the Kolmogorov-Smirnov test may result in drawing erroneous conclusions from your data. Additionally, you may want to consult the following references:

• Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. New York: John Wiley & Sons.
• D'Agostino, R. B. and Stephens, M. A., eds. 1986. Goodness-of-fit Techniques. New York: Dekker.
• Daniel, Wayne W. 1978. Applied Nonparametric Statistics. Boston: Houghton Mifflin.
• Daniel, Wayne W. 1995. Biostatistics. 6th ed. New York: John Wiley & Sons.
• Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.
• Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed. New York: W. H. Freeman and Co.
• Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed. Upper Saddle River, NJ: Prentice-Hall.