In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the number of degrees of freedom for treatments is given by:
A) k - 1.
B) n - k.
C) n - 1.
D) n - k + 1.

Question

Quizplus · Accepted Answer

The degrees of freedom for treatments is given by k - 1. This is because we need to estimate the variability due to treatments by comparing the means of different treatment groups. Once we know the means of k groups, we can calculate a grand mean, and then we need to estimate variability between the means and variability within the means. Since the total variability has n - 1 degrees of freedom (total sum of squares), and the within-group variability has n - k degrees of freedom (error sum of squares), we can obtain the degrees of freedom for treatments by subtracting the degrees of freedom for error from the total degrees of freedom, which is k - 1.

In the One-Way ANOVA Where K Is the Number of Treatments