Say you have three groups, and each group has 5 observations.
You can figure out if there is a significant difference between means with a simple one-way ANOVA.
I read in my nonparametric book, one can also permute the observations and conduct a permutation F-test. If $n_i = 5$, then the number of permutations is $\binom{15}{5,5,5} =756756$ permutations -- you need to calculate the F-value 756756 different times.
What is the point of doing a permutation F-test? Is it more accurate than a normal F-test???