F Test

---

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 detect before performing the F test whether your data violate any assumptions.
• Ways to examine F test results to detect assumption violations.
• Possible alternatives if 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:

• importance of homogeneity of variance
• Gaussian (normal) distribution assumption
• violation of assumptions

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 > σ_{2, or} σ₁ ≠ σ_2.
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.

---

Glossary | StatGuide Home | Home

---