For the following data,what is $S S _ { \text {between } }$ subjects? $$\begin{array} { l c c l c l }
& { \text { Treatments } } \
\text { Subject } & \text { I } & \text { II } & \text { III } & \text { P-totals } & \
\hline \text { A } & 3 & 4 & 5 & 12 & G = 27 \
\text { B } & 1 & 1 & 4 & 6 & \Sigma X ^ { 2 } = 109 \
\text { C } & 2 & 1 & 6 & 9 & \
& T = 6 & T = 6 & T = 15 & & \
& S S = 2 & S S = 6 & S S = 2 & &
\end{array}$$
A)2
B)3
C)6
D)12

Question

For the following data,what is $S S _ { \text {between } }$ subjects? $$\begin{array} { l c c l c l } 
& { \text { Treatments } } \
\text { Subject } & \text { I } & \text { II } & \text { III } & \text { P-totals } & \
\hline \text { A } & 3 & 4 & 5 & 12 & G = 27 \
\text { B } & 1 & 1 & 4 & 6 & \Sigma X ^ { 2 } = 109 \
\text { C } & 2 & 1 & 6 & 9 & \
& T = 6 & T = 6 & T = 15 & & \
& S S = 2 & S S = 6 & S S = 2 & &
\end{array}$$
A)2
B)3
C)6
D)12

Quizplus · Accepted Answer

To find the $SS_{\text{between}}$ for subjects, we use the formula:

$$SS_{\text{between}}=\sum_{i=1}^{k} \frac{T_i^2}{n_i}-\frac{G^2}{N}$$

where $k$ is the number of treatments, $T_i$ is the total score for treatment $i$, $n_i$ is the number of subjects in treatment $i$, $G$ is the grand total, and $N$ is the total number of subjects.

For this data, we have:

$$SS_{\text{between}}=\frac{6^2}{3}+\frac{6^2}{3}+\frac{15^2}{3}-\frac{27^2}{9}=2+6+18-81=-55$$

Since $SS_{\text{between}}$ cannot be negative, we set it to 0. Therefore, the best choice is C, 6.

For the Following Data,what Is SSbetween S S _ { \text {between } }SSbetween ​

For the Following Data,what Is $S S _ { \text {between } }$