Talk:Fisher transformation

Confidence Interval
The part "Definition" ends with "[...] can be used to construct a large-sample confidence interval for $$\rho$$ [...]". Shouldn't it rather be $$r$$ instead of $$\rho$$ as we defined $$\rho$$ previously to be the true correlation coefficient of the population? LoSchizzatore

No, a confidence interval is always estimating a population parameter (such as $$\rho$$). It is never used to estimate a sample statistic (such as $$r$$) because, given the data, we know the value of the statistic exactly. We need to estimate $$\rho$$ precisely because, being a population parameter, its true value is unknown.

Inverse hyperbolic function
I undid the change from "artanh" back to "arctanh". The inverse hyperbolic functions are called "area hyperbolic function", so "artanh" (= "area tanh") is not only the more common, but also the more fitting description than "arctanh" (= "arcus tanh"). see: http://en.wikipedia.org/wiki/Inverse_hyperbolic_function Jloh24 (talk) 10:19, 8 December 2011 (UTC)

Discussion
I am afraid I don't understand the meaning of the following sentence: "This is related to the fact that the asymptotic variance of r is 1 for bivariate normal data." I am not a statistician but I am guessing asymptotic means "for large sample sizes". Since r cannot go beyond -1 and +1, surely it can't have a variance of 1. Did the writer mean 1/n, do you think? Darrel Francis (talk) —Preceding undated comment added 21:23, 23 October 2012 (UTC)

Derivation POV
The Derivation section points out the the simplified form (i.e., arctanh) can easily be made much more accurate. However, it uses wording to indicate that this is obviously better (pushing a POV).

What is not at all clear is whether the more accurate form has a simple (preferably closed-form) inverse, or at least a simple very accurate approximation to the inverse. Without that, the simplified form has a very large advantage for many applications.

Is there a closed-form inverse to the more accurate form, or nearly so? If so, this article would benefit from inserting it. If not, the wording should be more neutral. Jmacwiki (talk) 23:36, 23 April 2018 (UTC)


 * Now reworded. Also, it is not clear what was meant by "[the near-constant variance is not the result of] the former property".  I have taken a guess at the intention of those words, but please repair if incorrect. Jmacwiki (talk) 14:41, 22 May 2018 (UTC)

clarify definition of r and rho
in the paper by Taraldsen both r and rho show up and also in this article. Couly you please provide the defining equations of both? 2A01:C23:8532:2200:9CB7:7A71:200E:91A1 (talk) 20:01, 27 July 2021 (UTC)

Definition vs. Derivation problem
Article states under "Definition" that the standard error of the transformed z = artanh(r) is 1/Sqrt(N-3). But under "Derivation", the article presents an expression for the variance: v = 1/N + 3/N^2 (when |ρ| is small and N is large).

The latter is not the square of the former, beyond first order in N. It appears that it should be. (The derivation asserts that the mean and variance expressions are more accurate than the simpler forms in the Definition section.)

If so, which one is correct, and what should the other be? If not, how are the stated standard error and the stated variance conceptually related, instead? Jmacwiki (talk) 23:03, 29 January 2023 (UTC)