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What is the difference between the two sets of statistic tests?

Which is recommended for finding out if the difference between groups is more significant than within groups, for non-parametric stable isotopic signature data?

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  • $\begingroup$ How exactly is data nonparametric? For those of us who are you know, statisticians and so not necessarily versed in your area, what's 'isotopic signature data' actually consist of? I presume it's relative concentrations of various isotopes in some kind of sample, but more info would help. $\endgroup$ – Glen_b Jun 5 '13 at 7:24
  • $\begingroup$ Since I assume this will be an unfamiliar term to more than just me: Link on ANOSIM. I see that the R package vegan can do this. $\endgroup$ – Glen_b Jun 5 '13 at 7:24
  • $\begingroup$ @Glen_b Although an isotope chemist might not agree, for all intents and purposes you can consider the data to range from -Inf to +Inf. Isotope ratios are in permille units and are the relative ratio of heavy to light isotope in a standard and in a sample. $\endgroup$ – Gavin Simpson Jul 5 '13 at 15:32
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ANOSIM was designed for multivariate responses, Kruskal-Wallis for a univariate response. ANOSIM converts the response to distances/dissimilarities and computes rank from those whereas Kruskal-Wallis ranks the observations themselves.

Unless you have multivariate responses (i.e. a matrix for $y$) then I would probably avoid ANOSIM. If you do then I would probably direct you to the adonis() function in the vegan R package as it does a multivariate form of ANOVA but using dissimilarities; it is generally considered a more robust approach than ANOSIM.

You will need to explain more about your specific data and hypothesis for us to be able to comment more.

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