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;
  • H1at 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:

image1 - Fieldman statistics
image1 – Fieldman statistics


  • 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.

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