# How to make correlation test with compositional data?

I have a compositional data set

> str(dfa)
'acomp' num [1:53, 1:4] 0.263 0.26 0.264 0.266 0.255 ...
- attr(*, "dimnames")=List of 2
..$$: chr [1:53] "3" "4" "5" "6" ... ..$$ : chr [1:4] "F" "H" "R" "T"


These are ratios of four skeletal elements to the sum of these four element lengths. I need to find out whether there are correlations between these ratios and absolute sum of sizes (in mm). It is not possible to make in a regular way. I have been trying to figure out, how to make it when we deal with compositional data (e.g. via balances: http://file.statistik.tuwien.ac.at/filz/papers/CorrMatG09.pdf), however it's quite hard for me, cause I'm weak in mathematics. I work in R. I would be extremely grateful if someone would be that kind and could sequentially tell me the procedures I have to carry out.

The last column is the sum size.

• Could you share (a link to) your data? ... and including that total (mm) variable. Start out, maybe with plotting the proportions against mm, and the look into the logratio transform – kjetil b halvorsen Jul 24 '20 at 16:49
• I've added the link to the data to the body of my question. I've tried what you say, yes, but I am not sure whether it is correct way or not. Dr. Aitchinson has pointed out that there are people he called "Null correlationists" and I am afraid to be of them :) When I test the ilr-transormed components on correlation with the sum size it is not that clear what am I testing according to my initial variables. Ok, my third ilr is ilr3=sqrt(3/4)*ln(T/(R * F * H)^(1/3)) (T,R,F and H are initial ratio variables). And it does negatively correlate with log (sum size), but is that real?) – Митя Васюков Jul 24 '20 at 17:08