When looking to establish a comparison on a small sample, especially to showcase data like consumer preferences or the relative effectiveness of various treatments, the Friedman test emerges as the apt solution.
The Friedman test is a statistical approach employed to compare several paired samples or repeated observations.
What is the Friedman test?
The Friedman test is a non-parametric statistical technique used to compare multiple paired samples or repeated observations. It is particularly beneficial when the prerequisites for conducting a ANOVA with repeated measures are not satisfied, particularly when the data do not conform to a normal distribution or when the sample size is too limited to assume normality.
This method utilizes the ranks attributed to the data instead of the data values themselves, rendering it resilient to extreme values or skewed distributions. Consequently, it is frequently employed in experimental studies where multiple treatments or conditions are imposed on the same subjects, such as in medical, psychological, or educational fields.
Practical example:
Imagine a researcher aiming to assess the effectiveness of three teaching methodologies (A, B, and C) to enhance the performance of a group of students. Each student is exposed to the three methods in random order, and their results are measured following each session.
Through the Friedman test, the researcher can compare the outcomes under each method to ascertain if there is a significant variance in student performance based on the applied method. Unlike a straightforward mean test, the Friedman test accounts for individual variations, as each student acts as a “control” for themselves.
Another example:
In a medical study context, a test compares the efficacy of three medications on patients with chronic migraines. Each patient undergoes all three treatments at different intervals, with the intensity of their pain recorded following each treatment. Again, the Friedman test will identify if any medication is significantly more effective than the others, considering individual differences.
To sum up, the Friedman test is an essential tool for analyzing repeated or correlated data, especially when the normality assumptions are in question.
When to apply the Friedman test?
Two factors justify using the Friedman test.
- Non-parametric data: data does not need to follow a normal distribution. A normal distribution (or bell curve) emerges when most values cluster around the mean. For instance, when measuring the height of 1,000 adults, most are expected to be around 1.70 m. In such cases, a test like ANOVA would be appropriate.
- Paired data: comparing two (or more) groups of participants on a particular test, where they are subjected to the same evaluations, for example, on beverages, homeopathic granules… Repeated measures are conducted on the same subjects – or objects.
The Friedman test generates rankings or scores. Since it can be applied to non-parametric data and offers more degrees of freedom, the Friedman test is more adaptable than the ANOVA test.
Examples of using the Friedman test
The Friedman test can be utilized to assess several options on the same individuals, objects, or scenarios, making it applicable across a wide range of sectors.
Scientific or medical research
Biologists can assess the effectiveness of several treatments on the same patients.
Marketing
A consumer panel evaluates the qualities of three smartphone prototypes or three ice cream flavors.
Education
Different teaching methods are tested on the same group of students.
Sports
The effectiveness of physical exercises is compared among several athletes.
What the Friedman test seeks to obtain?
Revisiting the examples mentioned before, distinct results are achieved in each scenario.
- A specific treatment is deemed more effective than the others,
- Consumers rank the ice creams or smartphones tested,
- Two of the teaching methods yield better outcomes than the others.
- A particular physical exercise markedly enhances the athletes’ physique.
Ranking and comparing
Therefore, the Friedman test helps determine if one option is superior or distinctly different from the others and can be applied to small samples, where the ANOVA test presumes a normal distribution for larger samples.
