Discussion
A completely randomized design has \(n\) plots and 10 treatments. While calculating the F-ratio for assessing equality of treatment effects, the experimenter forgot to divide the numerator and denominator sums of squares by corresponding degrees of freedom. But the statistician said that the calculated F-ratio is correct. Hence \(n\) is equal to :
Answer: D
\(n\) is 19.
In a completely randomised design with \(t = 10\) treatments and \(n\) plots, the F-ratio is
\[ \begin{aligned} F &= \frac{SS_{T}/(t - 1)}{SS_{E}/(n - t)} \\ &= \frac{n - t}{t - 1}\cdot\frac{SS_{T}}{SS_{E}} \end{aligned} \]
Forgetting both divisions gives \(SS_{T}/SS_{E}\), which equals the correct F exactly when \(n - t = t - 1\), that is
\[ n - 10 = 9 \Rightarrow n = 19 \]
With 10, 20 or 30 plots the error degrees of freedom would be 0, 10 or 20, not 9.
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