Permutation test for 3 samples or more?

Question

Algorithms

There is an experiment in which some of the respondents received an informational message in audio format, others - in the form of text with rhyme, and the latter received just a neutral text. Later they were asked about the content of the message, the answer was on a 10-point scale. I need to find out if there are differences in the answers to a question in three groups (audio, rhyme and text), using a permutation test. It is clear how it works in the case of two groups, but with more there are difficulties - what statistics to use? it must be sensitive to differences in at least two of the three groups. Tell me, how can I make a permutation test for more than 2 samples?

Answer 1

The test for detecting differences in the three groups is the so-called ANOVA test, i.e. a test to test for differences in variances.
Accordingly, the permutation test in this case should also simulate this test.
How to do it - you can see here https://math.stackexchange.com/questions/1189063/p...
Of course, I understand that you hardly ever programmed in R. But the sequence of actions there is quite clear, and Accordingly, it should not cause difficulties to shift this script to Python.
PS Just in case - ANOVA is implemented in Python using the f_oneway() function of the scipy.stats package