Question

What is$M{S}_{\text{between}}$?

Short answer

The value of$M{S}_{\text{between}}=8.58333$.

Step-by-step solution

Given Information

Team 1	Team 2	Team 3	Team 4
1	2	0	3
2	3	0	4
0	2	1	4
3	4	1	3
2	4	0	2

Explanation

To find the value of $M{S}_{\text{between}}$:

From our Table, we can calculate

$s_1=8,s_2=15,s_3=2,s_4=16$

We now can calculate:

${\mathbf{SS}}_{\text{between}}=\sum \left[\frac{{\left(s_j\right)}^2}{n_j}\right]-\frac{{\left(\sum s_j\right)}^2}{n}$

$S{S}_{\text{between}}=\frac{s_1^2}{5}+\frac{s_2^2}{5}+\frac{s_3^2}{5}+\frac{s_4^2}{5}-\frac{{\left(s_1+s_2+s_3+s_4\right)}^2}{20}$

$\text{where}{n}_1=n_2=n_3=n_4=5\text{and}n=n_1+n_2+n_3+n_4=20$

W calculate,

$\frac{(8{)}^2}{5}+\frac{(15{)}^2}{5}+\frac{(2{)}^2}{5}+\frac{(16{)}^2}{5}-\frac{(8+15+2+16{)}^2}{20}$

${\mathbf{SS}}_{\text{between}}=109,8-84.05=\mathbf{25}\mathbf{.}\mathbf{75}$

Calculate the Mean Sum of Squares between the groups

We calculate $M{S}_{\text{between}}$ like:

$M{S}_{\text{between}}=\frac{S{S}_{\text{between}}}{k-1}$

${\mathbf{MS}}_{\text{between}}=\frac{25.75}{3}=\mathbf{8}\mathbf{.}\mathbf{58333}$