Calculation of Degrees of Freedom
First we look at how to calculate the number of DOF for the numerator. In the numerator since we calculate the variance from the sample means, the number of samples matter. The degrees of freedom for the numerator is given by a general rule shown below:
(k - 1)
where k stands for the number of samples.
For the calculation of the number of DOF in the denominator, the number of elements within each sample play an important role. In each of the samples, we lose the discretion for specifying the last element. A general rule to find the number of DOF for the denominator is given by
nj denotes the number of elements in each of the sample and
S symbol indicating that we ought to take the sum of number of DOF of each sample.