Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.

$\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
6 & 7 & 9 & 11 \
8 & 10 & 11 & 14 \
10 & 11 & 12 & 15 \
12 & 12 & 13 & 16 \
14 & 15 & 15 & 19
\end{array}\end{array}$
-What is the group mean square?

Question

Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
6 & 7 & 9 & 11 \
8 & 10 & 11 & 14 \
10 & 11 & 12 & 15 \
12 & 12 & 13 & 16 \
14 & 15 & 15 & 19
\end{array}\end{array}$ ​
-What is the group mean square?

Quizplus · Accepted Answer

The group mean square (MS_groups) is calculated as the sum of squares between groups (SS_between) divided by the degrees of freedom between groups (df_between). First, calculate the overall mean and the means for each group:- Mean of A = (6 + 8 + 10 + 12 + 14) / 5 = 10- Mean of B = (7 + 10 + 11 + 12 + 15) / 5 = 11- Mean of C = (9 + 11 + 12 + 13 + 15) / 5 = 12- Mean of D = (11 + 14 + 15 + 16 + 19) / 5 = 15- Overall mean = (10 + 11 + 12 + 15) / 4 = 12Next, calculate SS_between:- SS_between = 5[(10 - 12)^2 + (11 - 12)^2 + (12 - 12)^2 + (15 - 12)^2] = 5[(4) + (1) + (0) + (9)] = 5 * 14 = 70Then, calculate df_between:- df_between = number of groups - 1 = 4 - 1 = 3Finally, calculate MS_groups:- MS_groups = SS_between / df_between = 70 / 3 = 23.33

Consider the Data Table Shown with Values for Five Individuals