A portion of an ANOVA summary table is shown below. Calculate the $F$-test value.
$\begin{array} { l c c } \text { Source } & \text { Sum of Squares } & \text { Degrees of Freedom } \ \text { Between } & 16 & 2 \ \text { Within (error) } & 43 & 31 \ \text { Total } & 59 \end{array}$

A) $5.77$
B) $0.17$
C) $41.66$
D) $0.37$

Question

A portion of an ANOVA summary table is shown below. Calculate the $F$-test value.
$\begin{array} { l c c } \text { Source } & \text { Sum of Squares } & \text { Degrees of Freedom } \ \text { Between } & 16 & 2 \ \text { Within (error) } & 43 & 31 \ \text { Total } & 59 \end{array}$

A) $5.77$
B) $0.17$
C) $41.66$
D) $0.37$

Quizplus · Accepted Answer

The $F$-test value is calculated by dividing the mean square between groups by the mean square within groups. Mean square is calculated by dividing the sum of squares by the degrees of freedom. For between groups, mean square = $16 / 2 = 8$. For within groups, mean square = $43 / 31 \approx 1.387$. Thus, $F = 8 / 1.387 \approx 5.77$.

A Portion of an ANOVA Summary Table Is Shown Below FFF

A Portion of an ANOVA Summary Table Is Shown Below $F$