Friedman's Test is a nonparametric
alternative to twoway
analysis of variance. The hypothesis
is:
H_{0} the means
of all the samples are equal
H_{1} the mean of at least one
of the samples is different
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 test involves:
 impose ranks on each of the columns.
If values are equal, average the ranks
they would have got if they were slightly
different:
Therapy 
Andrew 
Belinda 
Chris 
Dave 
Relaxed 
1 
1 
1.5 
1 
Normal 
2 
2 
3 
2.5 
High Intensity 
3 
3 
1.5 
2.5 
 calculate the F_{r} statistic
using the formula:
Where:
I 
Number of samples (treatments) 
J 
Number of blocks 
R_{i} 
sum of the ranks in row 'i' 
This gives a value for F_{r} of
4.65
The value of F_{r} has an approximately
chisquare
distribution with I  1 degrees
of freedom.
