# How to make correlation test with compositional data?

Cross Validated Asked on December 27, 2021

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.

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