In the completely randomized design of ANOVA where there are k treatments and n observations, the degrees of freedom for the F-statistic are equal to:
A) n and k
B) k and n
C) n - k and k - 1
D) k - 1 and n - k
E) n - 1 and k - 1

Question

Quizplus · Accepted Answer

The degrees of freedom for the F-statistic in a completely randomized design of ANOVA are calculated as follows:

- The numerator degrees of freedom is k - 1 because we are comparing the variation between the means of the different treatments (k groups) to the variation within each group. There are k groups, so the degrees of freedom for the numerator is k - 1.
- The denominator degrees of freedom is n - k because we estimate the within-group variance by calculating the variance of each group separately and averaging them. We lose one degree of freedom for each group when calculating within-group variance, so we subtract k from the total sample size n to obtain the degrees of freedom for the denominator, which is n - k.

Thus, the correct answer is D) k - 1 and n - k.

In the Completely Randomized Design of ANOVA Where There Are