Skip to main content
Log in

Sample size requirements for estimating pearson, kendall and spearman correlations

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a confidence interval having the desired width is examined. A two-stage approximation to the sample size requirement is shown to give accurate results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Caruso, J.C., & Cliff, N. (1997). Empirical size, coverage, and power of confidence intervals for Spearman's rho.Educational and Psychological Measurement, 57, 637–654.

    Google Scholar 

  • Cohen, J. (1988).Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Cohen, J., & Cohen, P. (1975).Applied multiple regression/Correlation analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • David, F.N. (1938).Tables of the ordinates and probability integral of the distribution of the correlation coefficient in small samples. Cambridge: Cambridge University Press.

    Google Scholar 

  • Desu, M.M., & Raghavarao, D. (1990).Sample size methodology. Boston, MA: Academic Press.

    Google Scholar 

  • Duncan, G.T., & Layard, M.W.J. (1973). A Monte-Carlo study of asymptotically robust tests for correlation coefficients.Biometrika, 60, 551–558.

    Google Scholar 

  • Dunlap, H.F. (1931). An empirical determination of the distribution of means, standard deviations, and correlation coefficients drawn from rectangular distributions.Annals of Mathematical Statistics, 2, 66–81.

    Google Scholar 

  • Fieller, E.C., Hartley, H.O., & Pearson, E.S. (1957). Tests for rank correlation coefficients. I.Biometrika, 44, 470–481.

    Google Scholar 

  • Fisher, R.A. (1925).Statistical methods for research workers. London: Hafner Press.

    Google Scholar 

  • Gardner, M.J., & Altman, D.G. (1986). Confidence intervals rather thanp-values: Estimation rather than hypothesis testing.British Medical Journal, 292, 746–750.

    Google Scholar 

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

    Google Scholar 

  • Hahn, G.J., & Meeker, W.Q. (1991).Statistical intervals: A guide for practitioners. New York, NY: Wiley.

    Google Scholar 

  • Haldane, J.B.S. (1949). A note on non-normal correlation.Biometrika, 36, 467–468.

    Google Scholar 

  • Kowalski, C.J. (1972). On the effects of non-normality on the distribution of the sample product moment correlation coefficient.Applied Statistics, 21, 1–12.

    Google Scholar 

  • Long, J.D., & Cliff, N. (1997). Confidence intervals for Kendall's tau.British Journal of Mathematical and Statistical Psychology, 50, 31–41.

    Google Scholar 

  • Looney, S.W. (1996). Sample size determination for correlation coefficient inference: Practical problems and practical solutions.American Statistical Association 1996 Proceedings of the Section on Statistical Education, 240–245.

  • Odeh, R.E., & Fox, M. (1991).Sample size choice (2nd ed.). New York, NY: Marcel Dekker.

    Google Scholar 

  • Pearson, E.S. (1929). Some notes on sampling tests with two variables.Biometrika, 21, 337–360.

    Google Scholar 

  • Pearson, E.S. (1931). The test of significance for the correlation coefficient.Journal of the American Statistical Association, 26, 128–134.

    Google Scholar 

  • Rider, P.R. (1932). The distribution of the correlation coefficient in small samples.Biometrika, 24, 382–403.

    Google Scholar 

  • Schmidt, F. (1996). Statistical significance testing and cumulative knowledge in Psychology: Implications for training of researchers.Psychological Methods, 1, 115–119.

    Google Scholar 

  • Stuart, A., & Ord, J.K. (1994).Kendall's advanced theory of statistics, Vol. 1, Distribution theory. New York, NY: Halsted Press.

    Google Scholar 

  • Zar, J.H. (1984).Biostatistical analysis (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bonett, D.G., Wright, T.A. Sample size requirements for estimating pearson, kendall and spearman correlations. Psychometrika 65, 23–28 (2000). https://doi.org/10.1007/BF02294183

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02294183

Key words

Navigation