In the one-factor case, Good and Lunneborg (2006) showed that the permutation test is superior to the analysis of variance. In the multi-factor case, simulations reveal the reverse is true. The analysis of variance is remarkably robust against departures from normality including instances in which data is drawn from mixtures of normal distributions or from Weibull distributions. The traditional permutation test based on all rearrangements of the data labels is not exact and is more powerful that the analysis of variance only for 2xC designs or when there is only a single significant effect. Permutation tests restricted to synchronized permutations are exact, but lack power.
Good, Phillip I.
"Analysis of MultiFactor Experimental Designs,"
Journal of Modern Applied Statistical Methods:
2, Article 2.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss2/2