Featured Article: Where to start...

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 for the Null Hypothesis σ₁ = 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.

Examine the glossary.

Back to StatGuide home page.

Get Adobe to read our PDF evaluation docs.

Satisfaction Guaranteed If you cannot edit At-PQC™ document(s) with your MS Office, OpenOffice or compatible cloud software program, we will fix it or refund your purchase. Can't find what you're looking for...? Please call, Fax or Email Us at: Cell-Phone Support 6:00am to 6:00pm. Home Page Click here to bookmark At-PQC™ then visit our Toolbox to find a quality control plan that will help you achieve an effective and efficient business infrastructure that focuses on customer satisfaction, continuous improvement and desirable cost savings. Visit with us today for comprehensive assistance in developing or choosing the right quality control plan for your business. Click here to visit our extensive selection of quality control plans, policies, procedures and forms or click here for help with where-to-start.

We can interact with you anywhere in the USA from 6:00am to 6:00pm Monday through Friday except holidays. JnF Specialties, LLC 664 Greenscape Lane Colorado Springs, Colorado 80916 Cellphone Support 6:00am to 6:00pm. Email Us at: Send an email to request support or call our helpline during your office hours. Click here to let us know how we're doing.

Get Adobe | About Us | Site Map | Contact Us | Privacy Policy

Policies | Procedures | FAA | Forms | Kits | ISO 9001 | Quality Plan

( quality control plan . com )