Based on my knowledge, permutation approach is suitable for the large sample data and at the same time this test does not rely on distribution assumption. However, I have some difficulties to make a statistical test of p-value. How to determine the p-value for permutation approach to the multi-group analysis?
You should enumerate all permutations of the data that are in agreement with your null hypothesis, and the p-value will be the proportion of permutations that give a test statistic greater than the one given by your data --- be careful if the test statistic is bilateral to include both sides.
Generally, there are too many permutations to enumerate them all; in that case, a big enough random sample of permutations will do the job.
The most difficult part is to define precisely what permutations are coherent with the hypothesis you test.
Note that the lmPerm package in R may help if you are using a linear model.
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