I’ve been having some concerns with the degrees of freedom R has been giving me from PERMANOVA (adonis), and I was hoping someone could shed some light on this. I have been looking over my R books and manuals, general statistics books for calculating DF, and surfed the stats forums but haven’t found any solid answers. I would really appreciate any help, truly.

To set the stage: My BCdist is run on invertebrate community data. I have a total of 35 samples, collected over 3 years. I have 2 experimental treatments (pesticide, no pesticide) and 6 plots per treatment. However, I have a missing value, for one of the treatments in one of the years (thus N = 35 rather than 36). To summarize:

Year 1: 6 pesticide plots, 6 no pesticide plots

Year 2: 5 pesticide plots, 6 no pesticide plots

Year 3: 6 pesticide plots, 6 no pesticide plots

N=35

I am interested in testing for Treatment, Year, and an interaction effect between Treatment * Year.

The code I used is: adonis(formula = BCdist ~ Treatment + Year + Treatment * Year, data = all, permutations = 999)

My output is as follows:

........................Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)

Treatment..........1 1.1103 1.11026 8.1168 0.16471 0.001 ***

Time..................1 0.8097 0.80966 5.9192 0.12011 0.001 ***

Treatment:Time...1 0.5806 0.58062 4.2448 0.08613 0.001 ***

Residuals............31 4.2403 0.13679 0.62905

Total.................34 6.7409 1.00000

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

I am not sure why my Year degrees of freedom are 1 considering I have 3 years. I have been trying to find a formula to confirm that my degrees of freedom are what they should be. If I use year DF = 2 (which I assumed it should be), and the residual DF formula “N – [(factor 1 df)x(factor 2 df)x(factor 1df X factor 2 df)]” I get Residuals = 31. This makes me think the two factor DFs from the table above must be wrong. Am I using the correct formula?

I am also unsure of how to proceed given a significant Trt x Year interaction; is there a multiple comparison permutation test, or do I need to subset my data and run a series of PERMANOVAs? Do I then have to Bonferroni-correct that series of PERMANOVAS? Again, thank you so much for your help!