Calculation for the Test of the Difference Between Two Independent Correlation Coefficients

I have been told to take a closer look at: http://www.quantpsy.org/corrtest/corrtest.htm but how exactly does this work?

E.g. Given two groups of data A and B, each with one explanatory variable and one response variable, each with e.g. n=20 data points, I can calculate Spearman's Correlation Coefficient SCC yielding SCC = 0.9 in group A and in group B I get SCC=-0.9.

From the above, it is obvious that in group A the data is well correlated with a slope >0 and in group B also well correlated, but with a slope <0, so definitely a difference - Right?

Now to the real question: The SCC quantifies in a non-parametric way how well correlated the explanatory and response variables are, but I am not sure I understand how it works with testing the difference between two correlations? I am thinking that testing SCC=0.3 and SCC=0.8 should not yield anything, since basically one correlation is rather weak and the other is sort of ok? But the link yields p=0.02

• The word "crappy" is widely regarded as vulgar slang. Words like "poor" or "weak" are better here just as they would be in theses, research reports or publications. – Nick Cox Mar 17 '15 at 19:21
• @NickCox : Edited accordingly. Sincere apologies for offence I may unintentionally have caused! English is not my native language. – LeonDK Mar 17 '15 at 19:59
• Note that Spearman's $r_{\text{S}}$ does not necessarily translate into a slope but into a monotonic association, the slope of which may be zero in places. Spearman's correlation measures how much knowing about $X$ tends to tell one about $Y$. Of course, if the relationship between $X$ and $Y$ is linear, Spearman's $r_{\text{S}}$ does give one the sign of that slope. – Alexis Mar 17 '15 at 20:23