I'm studying about analysis of variance and in my study material it was stated the following:
For the F-test in ANOVA, calculate the degrees of freedom as follows:
$$F(\alpha, \beta)$$
$\alpha$ is the degrees of freedom for variance between groups.
$\beta$ is the degrees of freedom for variance within groups.
$\alpha$ = number of groups $-1$
$\beta$ = total number of observations $-$ number of groups.
The definitions for $\alpha$ and $\beta$ were just defined as such with no further explanation. So my question is:
How do we arrive in the given definitions?