This isn't a strictly stats question--I can read all the textbooks about ANOVA assumptions--I'm trying to figure out how actual working analysts handle non-parametric data. I've gone through a lot of questions on this site looking for answers and I keep finding posts about when not to use ANOVA (in an abstract, idealized mathematical context) or how to do some of the things I describe below in R. I'm really trying to figure out what decisions people actually make and why.

I'm running analysis on grouped data from trees (actual trees, not statistical trees) in four groups. I've got data for about 35 attributes for each tree and I'm going through each attribute to determine if the groups differ significantly on that attribute. However, in a couple of cases, the ANOVA assumptions are slightly violated because the variances aren't equal (according to a Levene's test, using alpha=.05).

As I see it, my options are to: 1. Power transform the data and see if it changes the Levene p-val. 2. Use a non-parametric test like a Wilcoxon (if so, which one?). 3. Do some kind of correction to the ANOVA result, like a Bonferroni (I'm not actually sure if something like this exists?). I've tried the first two options and gotten slightly different results--in some cases one approach is significant and the other is not. I'm afraid of falling into the p-value fishing trap, and I'm looking for advice that will help me justify which approach to use.

I've also read some things that suggest that heteroscedasticity isn't really that big of a problem for ANOVA unless the means and variances are correlated (i.e. they both increase together), so perhaps I can just ignore the Levene's result unless I see a pattern like that? If so, is there a test for this?

Finally, I should add that I'm doing this analysis for publication in a peer-reviewed journal, so whatever approach I settle on has to pass muster with reviewers. So, if anyone can provide links to similar, published examples that would be fantastic.

This isn't a strictly stats question--I can read all the textbooks about ANOVA assumptions--I'm trying to figure out how actual working analysts handle data that doesn't quite meet the assumptions. I've gone through a lot of questions on this site looking for answers and I keep finding posts about when not to use ANOVA (in an abstract, idealized mathematical context) or how to do some of the things I describe below in R. I'm really trying to figure out what decisions people actually make and why.

I'm running analysis on grouped data from trees (actual trees, not statistical trees) in four groups. I've got data for about 35 attributes for each tree and I'm going through each attribute to determine if the groups differ significantly on that attribute. However, in a couple of cases, the ANOVA assumptions are slightly violated because the variances aren't equal (according to a Levene's test, using alpha=.05).

As I see it, my options are to: 1. Power transform the data and see if it changes the Levene p-val. 2. Use a non-parametric test like a Wilcoxon (if so, which one?). 3. Do some kind of correction to the ANOVA result, like a Bonferroni (I'm not actually sure if something like this exists?). I've tried the first two options and gotten slightly different results--in some cases one approach is significant and the other is not. I'm afraid of falling into the p-value fishing trap, and I'm looking for advice that will help me justify which approach to use.

I've also read some things that suggest that heteroscedasticity isn't really that big of a problem for ANOVA unless the means and variances are correlated (i.e. they both increase together), so perhaps I can just ignore the Levene's result unless I see a pattern like that? If so, is there a test for this?

Finally, I should add that I'm doing this analysis for publication in a peer-reviewed journal, so whatever approach I settle on has to pass muster with reviewers. So, if anyone can provide links to similar, published examples that would be fantastic.