In a one-way ANOVA with k groups, the degrees of freedom between treatments is

In a one-way ANOVA with k groups, the degrees of freedom between treatments is

• A. N - k
• B. N - 1
• C. k - 1
• D. k

Answer: (C)

In a one-way ANOVA, the between-treatments degrees of freedom measure how many independent comparisons you can make among the group means. There are k groups, so there are k group means, but they’re tied together by the grand mean. This linkage means only k minus 1 pieces of information about differences among the means are independent. So the between-treatments degrees of freedom is k − 1. For context, the total degrees of freedom is N − 1, and the within-treatments degrees of freedom is N − k, so the three pieces add up as df_total = df_between + df_within. The other values (N − k, N − 1, or k) don’t reflect the independent comparisons among the group means: N − k is for within-group variation, N − 1 is the total variation, and k would ignore the shared constraint imposed by the grand mean.

In a one-way ANOVA, the between-treatments degrees of freedom measure how many independent comparisons you can make among the group means. There are k groups, so there are k group means, but they’re tied together by the grand mean. This linkage means only k minus 1 pieces of information about differences among the means are independent. So the between-treatments degrees of freedom is k − 1.

For context, the total degrees of freedom is N − 1, and the within-treatments degrees of freedom is N − k, so the three pieces add up as df_total = df_between + df_within. The other values (N − k, N − 1, or k) don’t reflect the independent comparisons among the group means: N − k is for within-group variation, N − 1 is the total variation, and k would ignore the shared constraint imposed by the grand mean.