Hello--
Several months ago I inquired about the original reference for the
method/formula for testing the difference between independent correlation
coefficients. Thanks to those that responded with the Fisher references.
Below I list the references that are relevant. Several people suggested
that the 1921 paper is the reference, but after reading through them, the
idea is first developed in the 1915 paper.
My current question is, in the context of (applied) statistics, where does
Fisher's relation of
z = tanh^-1r (which is first stated in the 1915 paper)
become
z = .5[ln(1+r) - ln(1-r)]
which, I suppose, is more user friendly?
I realize they are mathematically equivalent, but when does then latter
become the formula of choice? Parenthetically, I should note that the more
common version of Fisher's r-to-z transformation is often incorrectly
printed as using the "log" rather than "natural log."
Regards,
Wil
References
----------
Fisher, R. A. (1915). Frequency distribution of the values of the
correlation coefficient in samples from an indefinitely large population.
Biometrika, 10, 507-521.
Fisher, R. A. (1921). On the probable error of a coefficient of
correlation deduced from a small sample. Metron, 1, 3-32.
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