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I'd like to know if it makes sense to use Spearman's correlation on my dataset. Below are plots between my 3 variables :

enter image description here

Correlation plot (Spearman): enter image description here

It seems it's pretty good but since I'm not from statistics I'm not sure. What do you think about it ?

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In general, Spearman checks for monotonicity, and so it can be used for discrete variables. Also, at least by eye, your top pair-plot does seem to indicate monotone decrease.

The problem, though, is that Spearman works by ranks, and so has a problem with ties. Your data seems to have many ties in the 5 values it obtains. In this case, you might want to use the Kendall tau-b test, which addresses this problem.

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    $\begingroup$ What do you mean specifically by Spearman has... problems with ties? (Kendall also has to manage "ties" in its own concept). What problems are these and how can they be managed. Could you expand on it or link to a discussion? Much thanks. $\endgroup$ – ttnphns Jul 7 '17 at 13:05
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    $\begingroup$ @ttnphns See, for example, here. This link describes the Kendall correction for ties in Spearman. There are several others, but please LMK if I'm missing something. $\endgroup$ – Ami Tavory Jul 7 '17 at 13:15

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