|
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.
|
