F distribution
The F distribution is the probability distribution associated with the f statistic.The f statistic, also known as an f value, is a random variable that has an F distribution.
Here are the steps required to compute an f statistic:
- Select a random sample of size n1 from a normal population, having a standard deviation equal to σ1.
- Select an independent random sample of size n2 from a normal population, having a standard deviation equal to σ2.
- The f statistic is the ratio of s12/σ12 and s22/σ22.
The following equivalent equations are commonly used to compute an f statistic:
f = [ s12/σ12 ] / [ s22/σ22 ]
f = [ s12 * σ22 ] / [ s22 * σ12 ]
f = [ Χ21 / v1 ] / [ Χ22 / v2 ]
f = [ Χ21 * v2 ] / [ Χ22 * v1 ]
where σ1 is the standard deviation of population 1, s1 is the standard deviation of the sample drawn from population 1, σ2 is the standard deviation of population 2, s2 is the standard deviation of the sample drawn from population 2, Χ21 is the chi-square statistic for the sample drawn from population 1, v1 is the degrees of freedomfor Χ21, Χ22 is the chi-square statistic for the sample drawn from population 2, and v2 is the degrees of freedom for Χ22 . Note that degrees of freedom v1 = n1 - 1, and degrees of freedom v2 = n2 - 1 .
For Calculation
let the value of s1 = a s2 =b σ1 = g σ2 =h Χ1 =y Χ2 =z v1 =c v2 =d
