# Interpretation of Spearman correlation for small sample

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

• 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? – Md. Ferdous Wahid May 2 '13 at 14:28
• 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. – Md. Ferdous Wahid May 2 '13 at 14:43