Discussion
In a completely randomized design with unequal group numbers, that is, \(n_{1} = 5\), \(n_{2} = 7\), \(n_{3} = 6\), what is the degrees of freedom for the error term ?
Answer: C
The error degrees of freedom are 15.
In a completely randomised design with \(k\) groups and \(N\) observations in all, the degrees of freedom split as total \(N - 1\), treatments \(k - 1\), error \(N - k\). Here
\[ \begin{aligned} N &= 5 + 7 + 6 = 18,\quad k = 3 \\ \text{error df} &= 18 - 3 = 15 \end{aligned} \]
Equivalently, each group contributes \(n_{i} - 1\): \(4 + 6 + 5 = 15\). Unequal group sizes do not change the formula.
17 is the total df \(N - 1\), 18 is \(N\), and 120 is not related to the design.
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