Question

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

Short answer

The completed ANOVA table is

$\begin{array}{|lllll|}\hline \text{source}& df& SS& MS=\text{SSIdf}& F=\text{statistic}\\ \text{Treatment}& 3& 2.124& 0.708& 0.75\\ \text{error}& 20& 18.880& 0.944& \\ \text{total}& 23& 21.004& & \\ \hline\end{array}$

Step-by-step solution

Given Information

Given data:

Explanation

Determine the degree of treatment freedom.

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

$0.708=\frac{2.124}{k-1}$

$\Rightarrow k-1=\frac{2.124}{0.708}$

$k-1=3$

Determine the total number of degrees of freedom.

$\text{total}df=\text{error}df-\text{treatment}df$

$=20+3$

$=23$

Explanation

Calculate the MSE error:

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

$0.75=\frac{0.708}{MSE}$

$MSE=0.944$

MSE (mean square error):

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

$SSE=MSE(n-k)$

$=0.944\left(20\right)$

$=18.88$

Calculate the total sum of squares (SST):

$SST=SSTR+SSE$

$=2.124+18.88$

$=21.004$