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

### Assumptions:

- Within each sample, the values are independent, and identically normally distributed (same mean and variance).
- The two samples are independent of each other.

### Guidance:

Ways to detectbefore performing the F test whether your data violate any assumptions.Ways to examineF test results to detect assumption violations.Possible alternativesif your data or F test results indicate assumption violations.

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 Hypothesisσ_{1} = σ_{2} (Normal Populations):

A test of the null hypothesis σ_{1} = σ_{2} based on the statistic F=s^{2}1/s^{2}2 (place the largest value in the numerator) depending on whether the alternative hypothesis is σ_{1} < σ_{2}, σ_{1} > σ_{2, or }σ_{1} ≠ σ_{2.}

In the first case the null hypothesis is rejected for F > Fα,n_{2}-1,n_{1}-1, in the second case it is rejected for F > Fα,n_{1}-1,n_{2}-1, and in the third case it is rejected for F > Fα,v_{1},v_{2} where v_{1} and v_{2} equal n_{2} - 1 and n_{1} - 1 when s_{2}2> s_{2}1 and n_{1} - 1 and n_{2} - 1 when s_{2}1 > s_{2}2

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.

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