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Seeing the FisherZ-transformation

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Abstract

Since 1915, statisticians have been applying Fisher'sZ-transformation to Pearson product-moment correlation coefficients. We offer new geometric interpretations of this transformation.

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References

  • Anderson, J.W. (1999).Hyperbolic Geometry. London: Springer-Verlag.

    Google Scholar 

  • Bridson, M.R., & Haefliger, A. (1999).Metric Spaces of Nonpositive Curvature. New York: Springer-Verlag.

    Google Scholar 

  • Brien, C.J., Venables, W.N., James, A.T., & Mayo, O. (1984). An analysis of correlation matrices: Equal correlations.Biometrika, 71, 545–554.

    Google Scholar 

  • Cannon, J.W., Floyd, W.J., Kenyon, R., & Parry, W.R. (1997). Hyperbolic geometry. In Levy, S. (Ed.)Flavors of Geometry (pp. 59–116). New York: Cambridge University Press.

    Google Scholar 

  • Casella, G., & Berger, R.L. (2002).Statistical Inference (Second Edition). Pacific Grove, CA: Duxbury.

    Google Scholar 

  • Fisher, R.A. (1915). Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population.Biometrika, 10, 507–521.

    Google Scholar 

  • Fisher, R.A. (1921). On the ‘probable error’ of a coefficient of correlation deduced from a small sample.Metron, 1, 3–32.

    Google Scholar 

  • Gayen, A.K. (1951). The frequency distribution of the product-moment correlation in random samples of any size drawn from nonnormal universes.Biometrika, 38, 219–247.

    Google Scholar 

  • Hawkins, D.L. (1989). Using U statistics to derive the asymptotic distribution of Fisher's Z statistic.The American Statistician, 43, 235–237.

    Google Scholar 

  • Hotelling, H. (1953). New light on the correlation coefficient and its transforms.Journal of the Royal Statistical Society B, 15, 193–225.

    Google Scholar 

  • Johnson, N.L., Kotz, S., & Balakrishnan, N. (1995).Continuous Univariate Distributions (Second edition: Volume 2). New York: Wiley.

    Google Scholar 

  • Lipsey, M.W., & Wilson, D.B. (2001).Practical Meta-Analysis. Thousand Oaks, CA: Sage.

    Google Scholar 

  • Rodgers, J.L., & Nicewander, W.A. (1988). Thirteen ways to look at the correlation coefficient.The American Statistician, 42, 59–66.

    Google Scholar 

  • Winterbottom, A. (1979). A note on the derivation of Fisher's transformation of the correlation coefficient.The American Statistician, 33, 142–143.

    Google Scholar 

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Correspondence to Charles F. Bond Jr..

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Bond, C.F., Richardson, K. Seeing the FisherZ-transformation. Psychometrika 69, 291–303 (2004). https://doi.org/10.1007/BF02295945

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  • DOI: https://doi.org/10.1007/BF02295945

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