Discussion
For a given data, the two-way ANOVA table is :
| Source | df | Ss | Mss | Fratio |
|---|---|---|---|---|
| Treat | 5 | 6 | - | c |
| Block | 3 | 4.5 | - | - |
| Error | a | 2.0 | - | |
| Total | 23 | 12.5 |
Hence the values of a, b and c are :
Answer: D
The values are \(a = 15\), \(b = 6.0\) and \(c = 9\).
Degrees of freedom add up, so the error df is \(a = 23 - 5 - 3 = 15\). The F ratio for treatments is the treatment mean square over the error mean square:
\[ \begin{aligned} \text{MS}_{\text{treat}} &= \frac{6}{5} = 1.2 \\ \text{MS}_{\text{error}} &= \frac{2.0}{15} = 0.1333 \\ c &= \frac{1.2}{0.1333} = 9 \end{aligned} \]
The letter \(b\) is not marked anywhere in the printed table; the value 6.0 in the keyed option matches the treatment sum of squares. In any case \(c\) decides the question, since only the last option has \(c = 9\). The values 1, 2.25 and 3 come from dividing the wrong mean squares or using sums of squares in place of mean squares (for instance 6/2 = 3).
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