I am currently being confused by different opinions regarding the spearman correlation interpretation. Some says, $\rho<0.2$ can be ignored as small/weak relationship, some says $\rho<0.1$, for sample size. I am explaining it here with examples.
Suppose, I have 29 samples with $x$ and $y$ features, $\rho_{x,y}=0.533$. I did two transformation on $y$ to make this relationship $<0.1$ and compare both transformation. This is to remove the influence (relationship) of $y$ with $x$. What I have obtained is
1) Transformation 1: $\rho_{y_{t1},x}=0.54$
2) Transformation 2: $\rho_{y_{t2},x}=-0.13$
For this small sample size can I safely conclude that transformation 2 successfully reduced the influences of $x$ on $y_{t2}$ (to make it almost independent of $x$)?
Thanks, Wahid
Best Answer
The correlation coefficient is what it is - basically an effect size measure - & any rules of thumb about what's 'small' or 'weak' ignore the context of what real things the variables are measuring. You can test for its statistical significance but its practical/theoretical significance is for a subject-matter expert to determine.
(Spearman's is a rank correlation coefficient, so those must be some pretty savage transformations you're doing - I can't imagine what or why.)