# What is an F Statistic?

The F Distribution is a continuous random sampling distribution with numerous applications. It is often used to test the ratio of two variances. If we let U have a Chi-Square distribution with v1 degrees of freedom, and we let V have a Chi-Square distribution with v2 degrees of freedom, then

has a F distribution with v1,v2 degrees of freedom.

The F Distribution has a mean of v2/(v2-2). The equation defining the F distribution curve is:

The F distribution has a shape which will be a function of the numerator and denominator degrees of freedom, v1 and v2.