Figure 6.3: Chi-square pdf with various degrees of freedom

The F-Distribution

If and are two independent Chi-square random variables with m and n degrees of freedom, respectively, then the following random variable follows F-distribution with m and n degrees of freedom.

From the previous discussion on Chi-square distribution it is clear that follows Chi-square distribution. Then, if two random samples of same size, n, are drawn from the two populations and the sample and population variances are , and , , respectively, the following random variable follows F-Distribution with n-1, and n-1 degrees of freedom;

This distribution is particularly useful in comparing the variances of two populations using the random samples obtained from them. Figure 6.4 shows the probability density functions of a random variable following F-distribution with various degrees of freedom.

Figure 6.4: F-distribution pdf for various degrees of freedom