Question

A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown below

Group A	Group B	Group C
101	142	107
109	158	105
97	147	197
105	111	201
103	132	168

That is the mean sum of squares within  MS_(Within)?

Answer 1

Solution-:

By using R-software:

> GrA=c(101,109,97,105,103);GrA
[1] 101 109 97 105 103
> GrB=c(142,158,147,111,132);GrB
[1] 142 158 147 111 132
> GrC=c(107,105,197,201,168);GrC
[1] 107 105 197 201 168
> d=stack(list(b1=GrA,b2=GrB,b3=GrC));d
values ind
1 101 b1
2 109 b1
3 97 b1
4 105 b1
5 103 b1
6 142 b2
7 158 b2
8 147 b2
9 111 b2
10 132 b2
11 107 b3
12 105 b3
13 197 b3
14 201 b3
15 168 b3
> names(d)
[1] "values" "ind"   
> av1=aov(values~ind,data=d)
> summary(av1)
Df Sum Sq Mean Sq F value Pr(>F)
ind 2 7169 3585 4.22 0.0409 *
Residuals 12 10193 849   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

From this output we get,

Mean sum of squares between, and

Mean sum of squares within,

R-code:

GrA=c(101,109,97,105,103);GrA
GrB=c(142,158,147,111,132);GrB
GrC=c(107,105,197,201,168);GrC
d=stack(list(b1=GrA,b2=GrB,b3=GrC));d
names(d)
av1=aov(values~ind,data=d)
summary(av1)