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  Critical Value of the Fisher F-Distribution

For a particular F-distribution and a particular probability level (alpha in the figure below), the critical value of the F-distribution is the point along the x-axis above which the total area under the curve is equal to the probability level -- The null hypothesis can be rejected for values of the test statistic that are larger than this critical value.

PROPERTIES

Some of the important properties of the Fisher F-distribution include:
  1. 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.
  2. 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.
  3. 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.
  4. The (central) F-distribution is a special case of the noncentral F-distribution.

ONLINE CALCULATOR

To calculate a critical value of the Fisher F-distribution, please click here.

CRITICAL VALUE TABLES

  1. To view a table of critical values of the Fisher F-distribution at a probability level of 0.01, please click here.
  2. For a table of critical values of the F-distribution at a probability level of 0.05, please click here.

FORMULAE

The formula involved in the computation of critical values of the Fisher F-distribution 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.
  
 
 
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