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  • $\begingroup$ Maybe something that maximizes the difference between a linear trend and a monotonic trend ? Perhaps, in R, x = 0:10 + 0.000000001; y = 1/x; plot(x,y); cor(x,y, method="pearson"); cor(x,y, method="kendall") . This can be run at: rdrr.io/snippets/ . Or change that decimal to e.g. 0.3 to make the plot more obvious. $\endgroup$ Commented Feb 1, 2022 at 21:04
  • $\begingroup$ thank you for the answer. I tried that but both methods return values of the same sign. I try to make opposite signs, when at least one value is significant $\endgroup$ Commented Feb 1, 2022 at 21:22
  • $\begingroup$ Your idea is fine. $\endgroup$
    – whuber
    Commented Feb 1, 2022 at 22:33