| Friedman's Test is a nonparametric
alternative to two-way
analysis of variance. The hypothesis
is:
H0 the means
of all the samples are equal
H1 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 Fr statistic
using the formula:
Where:
| I |
Number of samples (treatments) |
| J |
Number of blocks |
| Ri |
sum of the ranks in row 'i' |
This gives a value for Fr of
4.65
The value of Fr has an approximately
chi-square
distribution with I - 1 degrees
of freedom.
|
