Final answer:
The degrees of freedom for the numerator (between groups) in the one-way ANOVA are 2 and for the denominator (within groups) are 13, based on sample sizes of 7, 5, and 4.
Step-by-step explanation:
To determine the degrees of freedom for the F-statistic in a one-way ANOVA, you need to calculate two sets of degrees of freedom: one for the numerator (between groups) and one for the denominator (within groups).
The numerator degrees of freedom, often denoted as dfnum or dfbetween, is calculated as the number of groups minus one.
The denominator degrees of freedom, denoted as dfdenom or dfwithin, is the total number of observations across all groups minus the number of groups.
Given sample sizes of 7, 5, and 4 for the three groups, you add these values to get the total number of observations, which is 16 (7+5+4). Thus, using the formulae:
- dfnum = number of groups - 1 = 3 - 1 = 2
- dfdenom = total number of observations - number of groups = 16 - 3 = 13
The degrees of freedom for the F-statistic are therefore 2 for the numerator and 13 for the denominator.