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:
H_{0} The therapies all give
the same result
H_{1} 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 
F_{0}

pvalue 
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.
