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I'm assessing whether the relative abundance of bacterial communities are different across two treatments.

I have a control (n=3), a food compost treatment (n=3) and a biosolid compost treatment (n=3) that were added at three different timepoints (spring21, summer21, spring22). I want to determine if there are changes in the microbial community at different timepoints, treatments or an interaction of the two.

When I run a PERMONOVA there are significant differences for the timepoint and treatment factors but not an interaction of the two. I can also identify differences between different timepoints and treatments (Food compost is different than controls, spring21 is different than summer21, etc.) using pairwise comparisons. However, I also want to know if there is a particular sample (not which bacterium) that is responsible for these differences, one that is hugely different from the others. Which statistical test should I use?

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  • $\begingroup$ That's not readily subject to formal testing (and it looks like your data are already so limited that they can scarcely support the tests you have done), but the standard approach to this kind of sensitivity analysis is to systematically remove each observation from your dataset, refit the same model, and study relevant changes in the results. $\endgroup$
    – whuber ♦
    Commented May 1, 2023 at 17:56
  • $\begingroup$ "However, I also want to know if there is a particular sample (not which bacterium) that is responsible for these differences, one that is hugely different from the others. Which statistical test should I use?" - I doubt you'll be able to answer this with stats, on your dataset, but try visualising the data as a start and see if anything leaps out at you. $\endgroup$
    – Alex J
    Commented May 2, 2023 at 2:40

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