Advertisement

Journal of the Italian Statistical Society

, Volume 1, Issue 2, pp 289–294 | Cite as

The probability integral of the sample correlation coefficient

  • Luigi Greco
Notes

Summary

The probability integral (p.i.) values of the correlation coefficient in samples from a normal bi-variate population are usually computed by approximate methods, except for the first few values ofn. In this note we shall obtain the explicit expression for any sample size through a relation which also enables us to calculate easily and quickly the p.i. exact values as well as those of the density function (d.f.). From this p.i. expression it is also possible to obtain, among others, that of Student'st.

keywords

correlation coefficient probability distributions normal bi-variate populations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cramér H. (1946),Mathematical Methods of Statistics, Princeton University Press, Princeton, 398.zbMATHGoogle Scholar
  2. Fisher R. A. (1915), Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population,Biometrika, 10, 507–521.Google Scholar
  3. Garwood F. (1933), The Probability Integral of the Correlation Coefficient in Samples from a Normal Bi-variate Population,Biometrika, 25, 71–78.zbMATHGoogle Scholar
  4. Hotelling H. (1953), New Light on the Correlation Coefficient and its Transforms,J. Roy. Statist. Soc. B, 15, 193–232.MathSciNetGoogle Scholar
  5. Owen D. B. (1968), A Survey of Properties and Applications of the Noncentralt-Distribution,Technometrics, 10, 445–478.zbMATHCrossRefMathSciNetGoogle Scholar
  6. Soper H. E. et al. (1916), On the Distributions of the Correlation Coefficient in Small Samples. Appendix II to the Papers of “Student” and R. A. Fisher. A Cooperative Study,Biometrika, 11, 328–413.Google Scholar

Copyright information

© Societa Italiana di Statistica 1992

Authors and Affiliations

  • Luigi Greco
    • 1
  1. 1.Dipartimento di Economia e TerritorioUniversità di CassinoCassino (FR)Italy

Personalised recommendations