I have measurements of multiple metabolites from 4 treamtets X 2 species (each combination with several replicates)
After doing a 2 way ANOVA (considering the treatments and the species) for each of the metabolites, I have the p values of species effect and treatment effect on each metabolite (since there are multiple metabolites I correct those p values for multiple comparisons).
After correcting the p values, I would like to check the following:
1) For every case (i.e., each metabolite) significantly affected by speceis: At which of the treatments can this effect be observed (expecting to find at least one treatment where the 2 species significantly differ, since this was already indicated by ANOVA). THIS REQUIRES ONLY 4 COMPARISONS
2) For every case (i.e., every metabolite) significantly affected by treatment: which of treatments differ from each other, AT EACH species) (expecting to find at least one pair treatments significantly differing from each other, in at least one of the 2 species, since this was already indicated by ANOVA). THIS REQUIRES ONLY 12 COMPARISONS (6 treatment pairs X 2 species)
So according the results of the 1st analysis step (the ANOVA), I would like to dig in the data and perform ONLY 4, 12 or 16 (or 0) comparisons (and correct for multiple comparisons accordingly).
As far as I checked, a default test like Tukey will compare all the possible pairs in the setup which is 28 comparisons (requiring a very aggressive p value correction), most of which are of no interest (e.g, the differences between Species 1 in treatment A and species 2 in treatment C), or it can pool together one of the factors, while doing all the pairwise comparisons on the other factors (e.g., comparing only between the treatments, using the data from the 2 species together, and somehow taking into account the species effect), which is getting there but still not good enough (it might tell me that treatment A results in a higher value than treatment B, but I won't known whether this is true in both species).
So is there a known procedure for selective comparison, that takes the 2 way ANOVA model as its input? (preferably in R)
AND is there a non-parametric equivalent? (since not all the data is normally distributed, even applying common transformations)
*of course I can perform a t-test / wilcox-test between each two groups of interest "manually" but this neglects the overall experimental variance that is calculated in the ANOVA.
Thank you!
Sure the same ones unless you only select one comparison. See the attached.
Thank you David,
The PDF you attached explains methods of multiple testing pvalue corrections.
As I wrote, I prefer not to perform each of the desired comparisons "by myself" and correct the p-values (or the threshold).
Rather, what I'm looking a non-manual procedure whose inputs are (at least):
1) an ANOVA model that was fitted to some data
2) A specification of which pairwise comparisons to perform (out of all the comparison possible in the data)
T
he output should be the results of all the comparison (in approriately corrected pvalues or YES/NOs based on a defined and appropriately corrected pvalue)
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