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Friedman test

The Friedman test is used for testing the difference between three or more attributes of objects, characteristics of respondents or features of situations. The attributes are compared by ranking the values.

When is the Friedman test used?

This test is used for research questions like:
  1. Which part of the house is the most important aspect for buying a house, is it the living room, the bedroom or the kitchen?
  2. Do people appreciate the weather in winter, spring, summer and autumn differently?
  3. Do children prefer maths, language, biology or music lessons?

To apply the Friedman test you need to have three or more variables that have been measured at an ordinal, interval or ratio level. The values are ordered from high to low and per attribute summarized. Instead of using a lot of words, the example below makes this clear immediately.

Example of the Friedman test

In this example the rank scores are given, but it is no problem to start with continuous data. The values are going to be to be ranked anyway.

The formula of the Friedman test

If there would be no preferences, all W-scores would be the same. If that is not true, it can be tested if the scores differ significantly by applying this formula:

Formula of the Friedman test

As you can see, the result is a chi square value. And this calculated value is compared with the critical value of the chi square distribution. If this is abracadabra to you, I recommend you to read our manual about the statistical test procedure or to buy a good textbook about statistics.

Final remarks

The Friedman test doesn’t have any problems with ties. The ranking values then have to be equally divided over the attributes.

The Friedman test can be performed with small numbers. If there are a lot of objects, respondents or situations, say over 30, also a RM-ANOVA can be applied.

Related topics to Friedman test

  • Ordinal data 
  • Interval data 
  • Ratio data 
  • The normal distribution

Deepen your knowledge and read our manual about ...

  • How to choose the correct statistical test The statistical test procedure
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