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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

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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.)

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  • $\begingroup$ Thanks Scortchi for your reply. Although correlation coefficient itself is an effect size measure, different authors recommend different values to consider weak/none relationship. For example, according to this link, link, if the sample size is 25, 80% chance is that the true population $\rho$ is $0$ if the sample $\rho$ falls between $-0.26$ to $0.26$. Although, Spearman's is a rank correlation coefficient, we can use it for monotonic relationship dont we? $\endgroup$ – Md. Ferdous Wahid May 2 '13 at 14:28
  • $\begingroup$ Suppose you want to find the correlation between two variables which non-linear but monotonically related. If we use Pearson's correlation coefficient it would be smaller and misleading as you can see here, link. Thanks. $\endgroup$ – Md. Ferdous Wahid May 2 '13 at 14:34
  • $\begingroup$ Explaining a bit more. Suppose two variables, $x$ and $y$ are linearly related as, $y=mx$. So $y$ is always $m$ times of $x$. Now we transform $y$ as $y/x$ so that new variable $z=y/x=m$. This $z$ is then independent of $x$ and will have $0$ correlations. Please let me know if it is still not clear. $\endgroup$ – Md. Ferdous Wahid May 2 '13 at 14:43

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