Speaking Stata: Correlation with confidence, or Fisher's z revisited

Ronald Aylmer Fisher suggested transforming correlations by using the inverse hyperbolic tangent, or atanh function, a device often called Fisher’s z transformation. This article reviews that function and its inverse, the hyperbolic tangent, or tanh function, with discussions of their definitions and behavior, their use in statistical inference with correlations, and how to apply them in Stata. Examples show the use of Stata and Mata in calculator style. New commands corrci and corrcii are also presented for correlation confidence intervals. The results of using bootstrapping to produce confidence intervals for correlations are also compared. Various historical comments are sprinkled throughout.


Issue Date:
2008
Publication Type:
Journal Article
DOI and Other Identifiers:
pr0041 (Other)
PURL Identifier:
http://purl.umn.edu/122603
Published in:
Stata Journal, Volume 08, Number 3
Page range:
413-439
Total Pages:
27

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 Record created 2017-04-01, last modified 2017-08-26

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