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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.
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