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I have a data set where samples are collected once per year for 15 years at a number of sites. I am worried that these data are temporally autocorrelated and was trying to figure out if I need to address that. However, the only time I will be using degrees of freedom with these data is in a perMANOVA. This test calculates a pseudo F-statistic by permuting the rows. I can't figure out if the exchangebility assumption means that I don't need to worry about autocorrelation at all (i.e., permuting rows will simply destroy the temporal structure, which I am not interested in anyway) or if it means that I can't use a perMANOVA even if I accounted for autocorrelation?

Edit: I am editing this in the hopes that clarification will help get it answered. The perMANOVA user's guide says:

"Recall that for traditional one-way ANOVA, the assumptions are that the errors are independent, that they are normally distributed with a mean of zero and a common variance, and that the treatment effects are additive. In the case of a one-way analysis, the PERMANOVA test using permutations assumes only that the observation units are exchangeable under a true null hypothesis. There are no explicit assumptions regarding the distributions of the original variables; they are certainly not assumed to be normally distributed. However, implicit in the notion of exchangeability is the notion of independence, for if observations are correlated with one another (e.g., temporally or spatially), then randomly shuffling them will destroy this kind of inherent structure, if it is there. Thus, in general, we would assume that the observation units are independent of one another."

The meaning of this is ambiguous to me for the reasons stated in the first paragraph. I can't find any techniques for testing/correcting autocorrelation with perMANOVA, which maybe means that it isn't a problem to worry about?

User's guide: https://web.archive.org/web/20180806183841/https://pdfs.semanticscholar.org/4d0c/430f6129b427e48fb407e59ac79ee29b4cae.pdf

Original 2001 paper describing technique: https://web.archive.org/web/20180806184058/https://pdfs.semanticscholar.org/038e/8869b676aa365f2afdea935edf3f2003324d.pdf

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In the interest of closing up this question, I have received confirmation from a colleague that the correct interpretation is that permutation destroys the structure of autocorrelation.

I have bolded (in my original question) the passage in the user guide that is relevant to the answer.

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  • $\begingroup$ I am analysing a dataset of (most likely) spatially correlated data with PERMANOVA, as I am measuring the activity of bats throughout spatial transects across an ecotone. Your last response gave me some relief, and I share the same feeling about it, however, I can't find any reference to back up the claim that the permutation would 'destroy the structure of autocorrelation', as you said. Would you mind, if you had it, send that ref to me please? $\endgroup$ – user99730 Jan 5 '16 at 5:42
  • $\begingroup$ Eduardo - I have updated my original question and answer to clarify. The user guide is somewhat ambiguously stated if you have no other context to go off of. However, after having read more of Marti Andersons' papers (who I was never able to get ahold of) and consulted with stats folks at the university I was at, it appears that my answer is the right interpretation of the bolded passage. $\endgroup$ – HFBrowning Jan 14 '16 at 17:00

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