Unbalanced designs in PERMANOVA and Resampling Methods

#1
Hi there, I am looking for an answer to this very same question which was posted a long time ago and had no answer in here.
The original post was from a new member Yser but I have the same concern, does anybody can help with a though ?
"I am a new member here, working mainly in Ecology. I hope this is the right section to ask my question.

I am dealing with unbalanced designs (I am comparing groups with different sample sizes) in PERMANOVA (Permutational Multivariate Analysis of Variance). The PERMANOVA runs fine, and results are consistent with patterns I can observe in a NMDS or PCoA plot. But I would like to rule out any possible effect of the difference in size between my samples on the significant result I obtain. This is because one of my sample is half the size of the others. So my question is: How could I do that ?

I was thinking about a resampling method (bootstrapping) prior to the analysis, although I am not familiar with these. But then I realized there was an option in the software I am using (Primer Software) to calculate p-value using monte carlo approximation instead of permutations. I know that this option is meant to deal with small samples that don’t allow a sufficient number of permutations to calculate a p-value. In which case, monte carlo approximation is more suitable. But – please correct me if I am wrong - if this « monte carlo p-value » is based on a resampling method shouldn’t it already rule out the possible sample sizes effects in the result I obtain ? In which case I could just use the monte carlo approximation in the test instead of having to go through bootstraping.

I am really not familiar with resampling methods, so I might be completely wrong and any help would be much appreciated,

Thank you in advance


Yser"


Additionally, in PRIMER v7 there is a chance to save m-dimensional data to worksheet and I was thinking whether is fair or not to use those data as balanced replicates from the original data and run a second PERMANOVA to confirm results of unbalanced PERMANOVA under the "balanced" scenary of bootstrapped data obtained from the original ones that suppose to conserve the original sampling distribution

Thanks in advance
Alexis