| In the One
Way ANOVA example the five
replications within each row were all taken
under the same test conditions. Consider
the example where three treatments are evaluated
on four different patients:
| Therapy |
Andrew |
Belinda |
Chris |
Dave |
| Relaxed |
110 |
140 |
100 |
130 |
| Normal |
115 |
150 |
105 |
135 |
| High Intensity |
117 |
155 |
100 |
135 |
The hypothesis
is:
H0 The therapies all give
the same result
H1 At least one of the therapies
gives a different response
Use a level of significance of 0.05.
The patients are all different, and a 'One
Way ANOVA' would not cause the null hypothesis
to be rejected. However a two way ANOVA
separates the variation due to the therapy
from that due to different patient characteristics:
| Source
of Variation |
Sum
of Squares |
Degrees
of Freedom |
Mean
Square |
F0
|
p-value |
|
Therapy |
113.17 |
2 |
56.58 |
5.40 |
0.046 |
| Patient |
3832.67 |
3 |
1277.56 |
121.99 |
0 |
|
Error |
62.83 |
6 |
10.47 |
|
|
|
Total |
4008.67 |
11 |
|
|
|
The null hypothesis is rejected, the therapies
give different results at the 0.05 level
of significance.
|
