Appendix F:Percentage Points for the F-Distribution
Let W and Y be independent chi-square random variables with u and v degrees of freedom, respectively. Then the ratio
![bapp06-math-5001](/api/v2/epubs/9781118841792/files/images/bapp06-math-5001.jpg)
has the probability density function
![bapp06-math-5002](/api/v2/epubs/9781118841792/files/images/bapp06-math-5002.jpg)
This is the probability density for the F distribution with u degrees of freedom for the numerator and v degrees of freedom for the denominator and is denoted by Fu, v.
The percentage points of the F distribution are given in the following table. If be the percentage point of the F distribution with the numerator degrees of freedom of ν1 and the denominator degrees of freedom of ν2, then
![bapp06-math-5004](/api/v2/epubs/9781118841792/files/images/bapp06-math-5004.jpg)
The lower tail percentage points f1−a, u, v can be found using the following equation
![bapp06-math-5005](/api/v2/epubs/9781118841792/files/images/bapp06-math-5005.jpg)
![w9781118140673a6-1.jpg](/api/v2/epubs/9781118841792/files/images/w9781118140673a6-1.jpg)
![w9781118140673a6-2.jpg](/api/v2/epubs/9781118841792/files/images/w9781118140673a6-2.jpg)
![w9781118140673a6-3.jpg](/api/v2/epubs/9781118841792/files/images/w9781118140673a6-3.jpg)
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