, Volume 69, Issue 2, pp 291–303 | Cite as

Seeing the FisherZ-transformation

  • Charles F. BondJr.
  • Ken Richardson
Theory And Methods


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

Key words

correlation coefficient Fisher geometry hyperbolic transformation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, J.W. (1999).Hyperbolic Geometry. London: Springer-Verlag.Google Scholar
  2. Bridson, M.R., & Haefliger, A. (1999).Metric Spaces of Nonpositive Curvature. New York: Springer-Verlag.Google Scholar
  3. 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
  4. 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
  5. Casella, G., & Berger, R.L. (2002).Statistical Inference (Second Edition). Pacific Grove, CA: Duxbury.Google Scholar
  6. 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
  7. Fisher, R.A. (1921). On the ‘probable error’ of a coefficient of correlation deduced from a small sample.Metron, 1, 3–32.Google Scholar
  8. 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
  9. 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
  10. Hotelling, H. (1953). New light on the correlation coefficient and its transforms.Journal of the Royal Statistical Society B, 15, 193–225.Google Scholar
  11. Johnson, N.L., Kotz, S., & Balakrishnan, N. (1995).Continuous Univariate Distributions (Second edition: Volume 2). New York: Wiley.Google Scholar
  12. Lipsey, M.W., & Wilson, D.B. (2001).Practical Meta-Analysis. Thousand Oaks, CA: Sage.Google Scholar
  13. Rodgers, J.L., & Nicewander, W.A. (1988). Thirteen ways to look at the correlation coefficient.The American Statistician, 42, 59–66.Google Scholar
  14. Winterbottom, A. (1979). A note on the derivation of Fisher's transformation of the correlation coefficient.The American Statistician, 33, 142–143.Google Scholar

Copyright information

© The Psychometric Society 2004

Authors and Affiliations

  1. 1.Texas Christian UniversityUSA

Personalised recommendations