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When the data are not normal, how can the Spearman rank coefficient be interpreted differently from $R^2$?

As I understand it, when performing a rank correlation, the axes typically shouldn't show the actual raw data, but their ranks. However, I found this paper, DOI: 10.1183/13993003.00092-2016, Here: https://erj.ersjournals.com/content/48/2/484.long

where the graphs display the actual data, not their ranks, with the Spearman coefficient and $R^2$ (Graph D), also when performing the Mann Whitney test (Graph C), the axes don't display the ranks, but the raw data:

d) In both Löfgren's syndrome (LS) (black dots) and non-LS patients (open dots), co-expression of CXCR3 and CCR6 correlated with co-expression of T-bet and RORγT in BALF CD4+ T-cells (r=0.4593, p=0.0209 using non-parametric Spearman rank test; linear regression R2=0.2756, p=0.0070).

What is it that I am not understanding correctly?

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  • $\begingroup$ For a start Spearman correlation like almost any other correlation varies from $-1$ to $1$. That's isn't true of $R^2$ which cannot be negative. $\endgroup$
    – Nick Cox
    Commented Jun 9 at 20:31
  • $\begingroup$ The question in the title might be answered with stats.stackexchange.com/questions/8071/… $\endgroup$
    – Sextus Empiricus
    Commented Jun 9 at 21:54

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As I understand it, when performing a rank correlation, the axes typically shouldn't show the actual raw data, but their ranks

The computation is done with the ranks, but it is fine to present the data in a raw format. It is even more desirable. People want to see the original data and how the measurements have been. The graph (d) shows a lot more information, like values and range of the data.

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