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

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  • Nicholas J. Cox

    (Durham University, UK)

Abstract

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.

Suggested Citation

  • Nicholas J. Cox, 2008. "Speaking Stata: Correlation with confidence, or Fisher's z revisited," Stata Journal, StataCorp LP, vol. 8(3), pages 413-439, September.
    • Handle: RePEc:tsj:stataj:v:8:y:2008:i:3:p:413-439
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    References listed on IDEAS

    as
    1. Nicholas J. Cox, 2004. "Stata tip 15: Function graphs on the fly," Stata Journal, StataCorp LP, vol. 4(4), pages 488-489, December.
    2. Philip Ryan, 2004. "Stata tip 4: Using display as an online calculator," Stata Journal, StataCorp LP, vol. 4(1), pages 1-93, March.
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    Cited by:

    1. Stanislav Kolenikov, 2009. "Confirmatory factor analysis using confa," Stata Journal, StataCorp LP, vol. 9(3), pages 329-373, September.
    2. Patrick Royston & John B. Carlin & Ian R. White, 2009. "Multiple imputation of missing values: New features for mim," Stata Journal, StataCorp LP, vol. 9(2), pages 252-264, June.
    3. Geranda Notten & Julie Charest & Andrew Heisz, 2017. "Material deprivation in Canada," Working Papers 1715E, University of Ottawa, Department of Economics.
    4. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    5. Jaller, Miguel & Pineda, Leticia, 2017. "Warehousing and Distribution Center Facilities in Southern California: The Use of the Commodity Flow Survey Data to Identify Logistics Sprawl and Freight Generation Patterns," Institute of Transportation Studies, Working Paper Series qt5dz0j1gg, Institute of Transportation Studies, UC Davis.
    6. Héloise Cloléry & Guillaume Hollard & Fabien Perez & Inès Picard, 2022. "Should we trust measures of trust?," Working Papers 2022-13, Center for Research in Economics and Statistics.
    7. Tobias Keller & Martin Glaum & Andreas Bausch & Thorsten Bunz, 2023. "The “CEO in context” technique revisited: A replication and extension of Hambrick and Quigley (2014)," Strategic Management Journal, Wiley Blackwell, vol. 44(4), pages 1111-1138, April.

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