I read at http://davidmlane.com/hyperstat/A98696.html that
[W]hen the absolute value of the correlation in the population is low (say less than about 0.4) then the sampling distribution of Pearson's r is approximately normal. However, with high values of correlation, the distribution has a negative skew.
I understand that the point of the Fisher transformation is that the sampling distribution for the transformed value is more normal.
I have two (related) questions.
Why does this only happen for high values of r?
When we do significance tests we're typically wondering about the probability of obtaining our observed sample (or some extreme sample) if ρ=0. If we're doing that, what's the point of the transformation? The passage above stated that the sampling distribution was approximately normal if the correlation was weak, and there is no weaker correlation than 0.