Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-30T23:09:29.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Sample Size Requirements for Estimating Pearson, Kendall and Spearman Correlations

Published online by Cambridge University Press:  02 January 2025

Douglas G. Bonett  and
Thomas A. Wright
Douglas G. Bonett*
Affiliation:
Iowa State University
Thomas A. Wright
Affiliation:
University of Nevada, Reno
*
Requests for reprints should be sent to Douglas G. Bonett, Department of Statistics, Iowa State University, Ames, IA 50011.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

sample sizeinterval estimationcorrelationrank correlation
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 1 , March 2000 , pp. 23 - 28
Copyright
Copyright © 2000 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Caruso, J.C., & Cliff, N. (1997). Empirical size, coverage, and power of confidence intervals for Spearman's rho. Educational and Psychological Measurement, 57, 637–654CrossRefGoogle Scholar
Cohen, J. (1988). Statistical power analysis for the behavioral sciences 2nd ed., Hillsdale, NJ: Lawrence Erlbaum AssociatesGoogle Scholar
Cohen, J., & Cohen, P. (1975). Applied multiple regression/Correlation analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum AssociatesGoogle 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 PressGoogle Scholar
Desu, M.M., & Raghavarao, D. (1990). Sample size methodology. Boston, MA: Academic PressGoogle Scholar
Duncan, G.T., & Layard, M.W.J. (1973). A Monte-Carlo study of asymptotically robust tests for correlation coefficients. Biometrika, 60, 551–558CrossRefGoogle 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, 66–81CrossRefGoogle Scholar
Fieller, E.C., Hartley, H.O., & Pearson, E.S. (1957). Tests for rank correlation coefficients. I. Biometrika, 44, 470–481CrossRefGoogle Scholar
Fisher, R.A. (1925). Statistical methods for research workers. London: Hafner PressGoogle Scholar
Gardner, M.J., & Altman, D.G. (1986). Confidence intervals rather thanp-values: Estimation rather than hypothesis testing. British Medical Journal, 292, 746–750CrossRefGoogle ScholarPubMed
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, 219–247CrossRefGoogle ScholarPubMed
Hahn, G.J., & Meeker, W.Q. (1991). Statistical intervals: A guide for practitioners. New York, NY: WileyCrossRefGoogle Scholar
Haldane, J.B.S. (1949). A note on non-normal correlation. Biometrika, 36, 467–468CrossRefGoogle ScholarPubMed
Kowalski, C.J. (1972). On the effects of non-normality on the distribution of the sample product moment correlation coefficient. Applied Statistics, 21, 1–12CrossRefGoogle Scholar
Long, J.D., & Cliff, N. (1997). Confidence intervals for Kendall's tau. British Journal of Mathematical and Statistical Psychology, 50, 31–41CrossRefGoogle 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.Google Scholar
Odeh, R.E., & Fox, M. (1991). Sample size choice 2nd ed., New York, NY: Marcel DekkerGoogle Scholar
Pearson, E.S. (1929). Some notes on sampling tests with two variables. Biometrika, 21, 337–360CrossRefGoogle Scholar
Pearson, E.S. (1931). The test of significance for the correlation coefficient. Journal of the American Statistical Association, 26, 128–134CrossRefGoogle Scholar
Rider, P.R. (1932). The distribution of the correlation coefficient in small samples. Biometrika, 24, 382–403CrossRefGoogle Scholar
Schmidt, F. (1996). Statistical significance testing and cumulative knowledge in Psychology: Implications for training of researchers. Psychological Methods, 1, 115–119CrossRefGoogle Scholar
Stuart, A., & Ord, J.K. (1994). Kendall's advanced theory of statistics, Vol. 1, Distribution theory. New York, NY: Halsted PressGoogle Scholar
Zar, J.H. (1984). Biostatistical analysis 2nd ed., Englewood Cliffs, NJ: Prentice-HallGoogle Scholar