Question

Fill in the missing entries in the partially completed one-way ANOVA tables.

Short answer

The completed ANOVA table is

$\begin{array}{|lllll|}\hline \text{source}& df& SS& MS=SS/df& F=\text{statistic}\\ \text{Treatment}& 4& 37.84& 9.46& 1.464\\ \text{error}& 20& 135.20& 6.76& \\ \text{total}& 24& 173.04& & \\ \hline\end{array}$

Step-by-step solution

Given Information

Given data:

Explanation

Determine the total number of degrees of freedom. $totaldf=errordf+treatmentdf$

$=20+4$

$=24$

MSE (mean square error):

$MSE=\frac{SSE}{n-k}$

$SSE=MSE(n-k)$

$=6.76\left(20\right)$

$=135.2$

Explanation

Calculate the treatment's mean squares:

$MSTR=\frac{SSTR}{k-1}$

$=\frac{37.84}{4}$

$\Rightarrow MSTR=9.46$

$k-1=3$

Look for the$F-$static.

$F-\text{statistic}=\frac{MSTR}{MSE}$

$=\frac{9.46}{6.76}$

$=1.464$