Can you use Monte Carlo simulation to calculate sample size for a non-parametric test like a one way analysis of variance?

This particular question will get more traction on stats.stackexchange.com. Note that data are not parametric or nonparametric; tests are. And I assume you mean nonparametric ANOVA aka Kruskal-Wallis test, a generalization of the Wilcoxon test. I have never done a power calculation for Kruskal-Wallis; hope there are papers showing how. We often approximate the power by using parametric ANOVA power calculations.

For what itâ€™s worth, I believe the standard rank-based nonparametric methods may be wrong, or at least near-sighted. The designers of the standard nonparametric power tests did not make use of mathematically standard facts about permutations. For example Wassermanâ€™s nonparametric book makes no mention of normal subgroupsâ€”yet the lack of abelian parts is exactly what mathematicians say makes shufflings/permutations/reorderings different from numbers.

P. Diaconis picked up some representation theory in 1982 and wrote a book on itâ€”but nobody seems to have run with it afterwards.

Personally I donâ€™t find permutation tests very appealing. I like U-statistic theory that many rank tests are based on, but much better than that is to use semiparametric models that generalize nonparametric tests, allow for easier estimation on scales that users understand, and above all, allow for covariate adjustment. But this discussion is perfect for stats.stackexchange.com.