# F Test

The F test is used to test the null hypothesis that the two population variances corresponding to the two samples are equal.

### Guidance:

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

F Test:
A test based on a statistic that (under appropriate null hypothesis) has an F distribution; for example:

F Test for the Null Hypothesisσ1 = σ2 (Normal Populations):
A test of the null hypothesis σ1 = σ2 based on the statistic F=s21/s22 (place the largest value in the numerator) depending on whether the alternative hypothesis is σ1 < σ2, σ1 > σ2, or σ1 ≠ σ2.
In the first case the null hypothesis is rejected for F > Fα,n2-1,n1-1, in the second case it is rejected for F > Fα,n1-1,n2-1, and in the third case it is rejected for F > Fα,v1,v2 where v1 and v2 equal n2 - 1 and n1 - 1 when s22> s21 and n1 - 1 and n2 - 1 when s21 > s22

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 test may result in drawing erroneous conclusions from your data. Additionally, you may want to consult the following references:

• Brownlee, K. A. 1965. Statistical Theory and Methodology in Science and Engineering. New York: John Wiley & Sons.
• Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. New York: John Wiley & Sons.
• Daniel, Wayne W. 1978. Applied Nonparametric Statistics. Boston: Houghton Mifflin.
• Daniel, Wayne W. 1995. Biostatistics. 6th ed. New York: John Wiley & Sons.
• Hollander, M. and Wolfe, D. A. 1973. Nonparametric Statistical Methods. New York: John Wiley & Sons.
• Miller, Rupert G. Jr. 1996. Beyond ANOVA, Basics of Applied Statistics. 2nd. ed. London: Chapman & Hall.
• 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.