The Freidman hypothesis test looks at the difference between K groups of treatments (samples).
For run this test it’s important that:
- The K sample (from the different treatments) doesn’t need to come from a normal distribution;
- Data can be ordinal or continuous;
In this case the hypothesis are like:
- H0: all the k sample (treatments) have the same effect;
- H1: at least one sample (treatments) have a different effect.
The way to conduct the hypothesis test is like the one-sample t-tests, but we use another statistics.
The statistics used for this test is the one in image1:
- b is the number of indipendent block that is the single observation;
- k is the number of treatments;
- Ri is the sum of the rank for each sample. For an example on how to calculate the rank look the mann-whitney hypothesis test (step 1,2, 3).
We use the Chi-square distribution table for the critical value with a degree of freedom of k-1 and the alpha significance level.