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

$\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
11 & 12 & 11 & 16 \
12 & 13 & 14 & 18 \
14 & 14 & 15 & 19 \
15 & 17 & 16 & 23
\end{array}\end{array}$
-What is the group mean square?

Question

Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
11 & 12 & 11 & 16 \
12 & 13 & 14 & 18 \
14 & 14 & 15 & 19 \
15 & 17 & 16 & 23
\end{array}\end{array}$
-What is the group mean square?

Quizplus · Accepted Answer

The group mean square (also known as the mean square between groups) is calculated as the variance of the group means multiplied by the number of observations per group. First, calculate the mean of each group: A = (11+12+14+15)/4 = 13, B = (12+13+14+17)/4 = 14, C = (11+14+15+16)/4 = 14, D = (16+18+19+23)/4 = 19. The overall mean of these means is (13+14+14+19)/4 = 15. The sum of squares between groups (SSB) is calculated as the sum of the squared differences between each group mean and the overall mean, multiplied by the number of observations in each group: SSB = 4*((13-15)^2 + (14-15)^2 + (14-15)^2 + (19-15)^2) = 4*(4 + 1 + 1 + 16) = 4*22 = 88. The degrees of freedom between groups (dfB) is the number of groups minus one, which is 4-1 = 3. The group mean square is then SSB/dfB = 88/3 = 29.33.

Consider the Data Table Shown with Values for Six Individuals