The Friedman Non Parametric hypothesis test is an alternative to the one-way ANOVA with repeated measures. Friedman test was developed by the American economist Milton Friedman.

The Friedman Non Parametric hypothesis test is to test for differences between groups (three or more paired groups) when the dependent variable is at least ordinal. Friedman test is preferred when compared to other non parametric tests in a situation where the same parameter has been measured under different conditions on the same subject. Example: Patient Serum content monitoring before treatment, after one month, and after three months of treatment.

Friedman’s test is similar to the Kruskal-Wallis Test and also an extension of the sign test. This test is the best statistic to use for a repeated measures type of experiment to determine if a particular factor also has an effect.

The Friedman test is to test whether the k paired samples (k>2) of n size, are from the same population or the samples from populations having similar properties, considering the position parameter.

**Assumptions of the Friedman Test**

- The group is a random sample from the population
- No interaction between blocks (rows) and treatment levels (columns)
- The one group that is measured on three or more different occasions
- Data should be at least an ordinal or continuous
- The samples are do not need to be normally distributed

**Procedure to conduct Friedman Test**

- Rank each row (block) together and independently of the other rows. When there are ties, the average ranks of the observations.
- Sum the ranks for each column (treatments) and then sum the squared columns’ total
- Compute the test statistic
- Determine critical value from the Chi-Square distribution table with k-1 degrees of freedom
- Formulate decision and conclusion

**Calculation of Friedman Non Parametric Hypothesis Test **

The test statics of Friedman’s test is

where R_{j} is the sum of the ranks for sample j.

n is the number of independent blocks

k is the number of groups or treatment levels

DF= number of groups -1 (k-1)

- Null Hypotheses H
_{0}: Median treatment effects of the population are all the same - Alternative Hypotheses H
_{1}: There is a difference in treatment effects.

## Example of Friedman Non Parametric Hypothesis Test

Department of Public health and safety monitors whether the measures taken to clean up drinking water were effective. Trihalomethanes (THMs) in 12 counties drinking water compared before cleanup, 1 week later, and 2 weeks after cleanup.

- Null
Hypothesis H
_{0}= the cleanup system had no effect on the THMs - Alternative Hypothesis H1= the cleanup system effected the THMs

Significance level α=0.05

Calculate
the R_{j}

Q=20.16

For the values of independent blocks (n) greater than 20 and/or values of groups (k) greater than 6, use χ^{2} table with k-1 degrees of freedom otherwise use the Friedman table

The calculated Q value is greater than the critical value of Q for a 0.05 significance level. Q_{calculated }>Q_{critical} hence reject the null hypotheses.

So, it is concluded that the cleanup system effected the THMs of drinking water

**Six Sigma Black Belt Certification Friedman Non Parametric Test Questions:**

**Question:** A psychologist monitored the same group of students’ reactions while watching comic films and compared the students’ reactions when watching political and drama films. The tabulated data is skewed. Which of the following test to be used to analyze the data?

(A) Mood’Median test

(B) Kruskal-Wallis test

(C) Mann-Whitney U test

(D) Friedman Test

**Answer: **

**D: ** The Friedman test is to test for differences between groups when the dependent variable is at least ordinal. It is used to compare three or more matched or paired groups.

## Comments (7)

Second video is unavailable

Thanks, Lori. I’ve removed the missing video.

Como é determinada a significância do teste?

Excellent

Glad you like it, Murad.

What about friedman but on case of ties

Hi Abdul,

When ties occur in the Friedman test, one common approach is to assign tied observations the average rank of the tied ranks. This is known as the average rank method.

In the above example, counties 3 and 6 have ties, we took the average ranks.

Thanks