Confidence interval for correlation I know the confidence interval of an estimated correlation can be calculated after performing Fisher transformation. 
But I never figured out why. I also couldn't find the explanation online. Can someone point me to the right direction? 
 A: Nick Cox has a really good explanation in a 2008 Speaking Stata column from SJ that I will excerpt here:

pwcorr [DVM: Stata's pairwise correlation command] offers only a $p$-value from the
  standard $t$ test of whether the population correlation $\rho$ is really
  zero. .... The latter $t$ test cannot be converted into useful
  confidence intervals, because once the population correlation is
  really not zero, the sampling distribution of estimates $r$ is
  substantially skewed, even for large sample sizes. That should not
  seem surprising, given that correlations are constrained to fall
  within $[−1, 1]$. Getting at the form of the distribution is a messy
  problem with, for the most part, only complicated exact solutions, but
  for practical data analysts an attractive way forward is offered by a
  suggestion of Ronald Aylmer Fisher (1890–1962): even though $r$ usually
  has an awkward skewed distribution, the inverse hyperbolic tangent, or
  atanh, of $r$ is much better behaved. This transform, within statistics
  often labeled Fisher’s $z$, is said to be normally distributed to a good
  approximation. The basic tactic is now evident: apply standard
  normal-based technique on the $z$ scale, and then back-transform using
  its inverse transform, the hyperbolic tangent, or tanh.

Bootstrapping is a more modern alternative to the classical transformation approach.
