Statistics Knowledge Base - p-Value for the Fisher F-Test

Thursday, August 28, 2008

p-Value for the Fisher F-Test

The p-value (alpha in the figure below) for a one-tailed Fisher F-test is the probability that a value chosen at random from a particular F-distribution would be greater than or equal to the value of an observed value (the F-value) from the same distribution.

PROPERTIES

Some of the important properties of the Fisher F-distribution include:

Because the Fisher F-distribution is a probability distribution, the p-value for a one-tailed F-test also refers to the total area under a particular F-distribution from the F-value to infinity.
The shape of an F-distribution depends upon its numerator and denominator degrees of freedom. As the degrees of freedom increase, the shape of the F-distribution approaches the normal distribution.
The F-distribution is directly related to the chi-square distribution, insofar as the F-distribution is a function of the ratio of two independent chi-square variates which have been divided by their respective degrees of freedom.
The (central) F-distribution is a special case of the noncentral F-distribution.

ONLINE CALCULATOR

To calculate a p-Value for the Fisher F-Test, please click here.

INTERACTIVE PROBABILITY VALUE EXPLORATION

To explore probability values for the Fisher F-distribution in an interactive 3-D environment, please click here (requires Adobe Flash).

PROBABILITY VALUE TABLES

I have Fisher F-distribution probability tables available for F-values of 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0.

FORMULAE

The formula involved in the computation of a p-Value for the Fisher F-test is detailed below.

F-distribution probability density function:
Where d₁ and d₂ are the numerator and demoninator degrees of freedom, and B is the Beta function.

REFERENCES

David, F.N. (1949), "The Moments of the z and F Distributions", Biometrika, vol. 36, pp. 394-403.

Abramowitz, M. and Stegun, I.A., eds. (1965), "Handbook of Mathematical Functions", Dover, New York, NY.