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I have a list of values $S$. I want to compare the Spearman correlations of $S$ with $N$ other lists of values $O_k$ ( $k∈[N]$ ). The lists $O_k$ are not independent. Each value $O_k^j$ ( $j∈[|O_k|]$ ) in $O_k$ is correlated with the corresponding value $O_{k+1}^j$ in $O_{k+1}$.

If the lists were independent, I assume I could use standard multiple comparisons corrections to adjust my $\alpha$ for significance testing - but my intuition is that this would be too conservative given the dependences between the lists. Is there a suitable method for setting my $\alpha$ in this case? Does it depend on the nature of the dependence between the $O_k$s?

I found this related question: Comparing two dependent Spearman's rank correlation coefficients but I'm not sure the answer helps me (especially as I can't get behind the linked article paywall...)

PS: apologies for any sloppy notation......

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Bonferonni correction can indeed be too stringent. Instead you can construct a null-distribution of correlation values between your variables, and look whether you can reject the null-hypothesis when you randomly swap them. Check the following https://youtu.be/I0qoP7yvP-4

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  • $\begingroup$ Thanks @c0s1n3! Thats the sort of thing I was looking for and makes sense. $\endgroup$
    – Richard Tomsett
    Commented Jul 24, 2019 at 13:07

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